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3 5 6 A B C D E F G H I J K L M N O P Q R S T U V W Z

1. Mathematical millionaire?
   Plus Online Maths Magazine: News Story
    [ TOPOLOGY ] 


2. Career interview: Architect
   Wen Quek works for an award-winning architectural cooperative based in London. Recently, she worked on the new library at the University of Cambridge's Centre for Mathematical Sciences. As she tells Plus, Wen sees many parallels between mathematics and architecture.
    [ ARCHITECTURE ] 


3. Puzzle page
   Plus Online Maths Magazine: Regular Item
    [ ALGEBRA ] 


4. Puzzle page
   Plus Online Maths Magazine: Regular Item
    [ ALGEBRA ] 


5. Puzzle page
   Plus Online Maths Magazine: Regular Item
    [ ALGEBRA ] 


6. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHS EDUCATION ] 


7. Outer space: Monkey business
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 


8. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

3

3-BODY PROBLEM

1. Outer space: Two's company, three's a crowd
   Plus Online Maths Magazine: Regular Item
    [ MECHANICS ] 


2. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

3N+1 CONJECTURE

1. More hailstones...
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

Back to the top

5

5-BODY PROBLEM

1. Outer space: Two's company, three's a crowd
   Plus Online Maths Magazine: Regular Item
    [ MECHANICS ] 

Back to the top

6

6174

1. Mysterious number 6174
   6174 is a very mysterious number. Yutaka Nishiyama explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.
    [ NUMBER THEORY ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN SPORT ] 

Back to the top

A

ABEL PRIZE

1. And the winner is ...
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. En-Abeled
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Count-abel even if not solve-abel
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 


4. A differential story
   Plus Online Maths Magazine: News Story
    [ ABEL PRIZE ] 


5. Abel to iPod
   Plus Online Maths Magazine: News Story
    [ ABEL PRIZE ] 

ACCOUNTANCY

1. Career interview - Accountant
   We talk to Tim Pilkington, a keen basketball player, who has a joint honours BSc in Maths, Physical Education and Sports Science from Loughborough University. Tim has worked as a mathematics teacher and is now working as an accountant.
    [ FINANCIAL MATHEMATICS ] 

ACCOUNTING

1. Career interview: Freelance IT consultant
   Jason Winborn specialises in human resource management software Peoplesoft, and has been working freelance as a consultant for four years.
    [ IT ] 

ACHILLES PARADOX

1. Mathematical mysteries: Zeno's Paradoxes
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 

ACOUSTIC OSCILLATION

1. Stellar heartbeats
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

ACTION AT A DISTANCE

1. Cracking codes, part II
   In the second of two articles, Artur Ekert visits the strange subatomic world and investigates the possibility of unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 

ACTUARIAL MATHEMATICS

1. Career interview - Actuarial Student
   Find out about what it is like to work as an actuary with Watson Wyatt Partners Worldwide. There's also salary information and a careers contact point.
    [ FINANCIAL MATHEMATICS ] 


2. What a coincidence!
   Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.
    [ PROBABILITY ] 


3. Death and statistics
   Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
    [ FINANCIAL MATHEMATICS ] 


4. Career Interview: Actuary
   Actuaries use mathematics to model the real world, finding business solutions to the perennial problems thrown up by life's uncertainties. Kathy Byrne tells Plus about life as Actuarial Director of an Insurance Company.
    [ FINANCIAL MATHEMATICS ] 


5. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 

ADAM SMITH

1. Adam Smith and the invisible hand
   Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
    [ FINANCIAL MATHEMATICS ] 

ADAMS PRIZE

1. Woman joins Adams family
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

ADRIAN SMITH

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


3. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


4. Teaching excellence
   Plus Online Maths Magazine: News Story
    [ MATHS EDUCATION ] 

ADVECTION-DIFFUSION EQUATION

1. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

AERODYNAMICS

1. Understanding turbulence
   Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
    [ FLUID MECHANICS ] 


2. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 

AERONAUTICS

1. Career interview: Military air traffic controller
   Geoff Wilson is an air traffic controller for the Royal Air Force. Recently back from Kabul in Afghanistan, he tells Plus how logical thinking under pressure is crucial in his job.
    [ MANAGEMENT ] 

AESTHETICS

1. The golden ratio and aesthetics
   It was Euclid who first defined the Golden Ratio, and ever since people have been fascinated by its extraordinary properties. Find out if beauty is in the eye of the beholder, and how the Golden Ratio crosses from mathematics to the arts.
    [ MATHEMATICS AND THE ARTS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS AND THE ARTS ] 

AFRICAN PICTOGRAM

1. New designs from Africa
   Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
    [ GEOMETRY ] 

AIRCRAFT WAKE VORTEX

1. Career interview: Aerodynamicist
   Plus talks to Christine Hogan, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team.
    [ AERODYNAMICS ] 

AIRLINE PRICING

1. I'm not paying that!
   It's not that long ago that all you needed to run an airline was a few planes and some competent pilots. But now, with more of us zipping around the globe every year and the advent of no frills airlines, keeping an airline competetive has become a complicated business. Christine Currie explains how your airfare is calculated.
    [ OPERATIONS RESEARCH ] 

ALAN TURING

1. Exploring the Enigma
   During the Second World War, the Allies' codebreakers worked at Bletchley Park to decipher the supposedly unbreakable Enigma code. Claire Ellis tells us about their heroic efforts, which historians believe shortened the war by two years.
    [ CRYPTOGRAPHY ] 

ALGEBRA

1. Against the odds
   Danielle Stretch looks back at the remarkable life of pioneering mathematician Emmy Amalie Noether (1882-1935). Despite her constant struggles to make her way in a man's world, she made significant contributions to the development of modern algebra.
    [ HISTORY OF MATHEMATICS ] 


2. The power of groups
   Groups are some of the most fundamental objects in maths. Take a system of interacting objects and strip it to the bone to see what makes it tick, and very often you're faced with a group. Colva Roney-Dougal takes us into their abstract world and puzzles over a game of Solitaire.
    [ GROUP THEORY ] 


3. An enormous theorem: the classification of finite simple groups
   Plus Online Maths Magazine: Feature Article
    [ GROUP THEORY ] 

ALGEBRAIC GEOMETRY

1. Struggling for sixteen
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

ALGEBRAIC NUMBER

1. Mathematical mysteries: Transcendental meditation
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

ALGORITHM

1. Pilgrims, planes and postage stamps
   Practical problems often have no exact mathematical solution, and we have to resort to using unusual techniques to solve them. From navigation in the 17th century to postage stamps, see how this principle applies to a variety of real-life problems - and also learn how to use a piece of string to locate a German bomber!
    [ ENGINEERING ] 


2. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


3. Why Was The Computer Invented When It Was?
   Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
    [ COMPUTER SCIENCE ] 


4. Howzat!
   Numbers are bandied around all the time in sports coverage - and cricket is particularly rich in statistics and rankings. It has probably not escaped your attention that the World Cup of cricket has just finished in South Africa (Australia won - again) and so to mark the occasion, Rob Eastaway tells Plus what it takes to be the best.
    [ MATHEMATICAL MODELLING ] 


5. CAPTCHA if they can
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

ALIEN LIFE

1. Life as we don't know it
   Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
    [ ASTROBIOLOGY ] 

ALMA

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

ALTRUISM

1. Mathematical mysteries: Survival of the nicest?
   Plus Online Maths Magazine: Regular Item
    [ GAME THEORY ] 

AM (AMPLITUDE MODULATION)

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 

ANALOGUE COMPUTER

1. Why Was The Computer Invented When It Was?
   Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
    [ COMPUTER SCIENCE ] 

ANALYSIS

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 


2. Count-abel even if not solve-abel
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

ANALYTICAL ENGINE

1. Ada Lovelace - visions of today
   Rachel Thomas looks at the life and work of pioneering woman mathematician Ada Lovelace, who foresaw computer-generated music and graphics, despite living long before the computer era.
    [ COMPUTER SCIENCE ] 

ANAMORPHIS

1. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

ANGLE TRISECTION

1. Mathematical Mysteries: Trisecting the Angle
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


2. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 

ANGULAR DISTANCE

1. Analemmatic sundials: How to build one and why they work
   We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.
    [ GEOMETRY ] 

ANGULAR FORCE

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 


2. In skimming, spin's the thing
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

ANGULAR VELOCITY

1. Outer space: Wagons Roll
   Plus Online Maths Magazine: Regular Item
    [ MECHANICS ] 

ANIMAL PATTERNING

1. How the leopard got its spots
   How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Lewis Dartnell solves these, and other, puzzles of animal patterning.
    [ DIFFERENTIAL EQUATIONS ] 

ANNUITY

1. Death and statistics
   Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
    [ FINANCIAL MATHEMATICS ] 

ANTHROPIC PRINCIPLE

1. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 

ANTHROPOLOGY

1. Not just knots: the secrets of khipu
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

APERIODIC TILING

1. From quasicrystals to Kleenex
   This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.
    [ GEOMETRY ] 


2. Roger Penrose: A Knight on the tiles
   Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
    [ THEORETICAL PHYSICS ] 

APHELION

1. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 

ARBITRAGE

1. Rogue trading?
   The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
    [ FINANCIAL MATHEMATICS ] 

ARCHAEOLOGY

1. Not just knots: the secrets of khipu
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

ARCHITECTURE

1. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 

ARITHMETIC

1. Mathematical mysteries: The Solitaire Advance
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 


2. The death of the lightning calculator
   Plus Online Maths Magazine: Feature Article
    [ ARITHMETIC ] 


3. Outer space: Tally ho!
   Plus Online Maths Magazine: Regular Item
    [ HISTORY OF MATHEMATICS ] 

ARITHMETIC CODING

1. Dashing along
   Currently, disabled computer users have a hard time inputting text, using laborious word-completion. Plus find out how this is changing, thanks to Dasher, a new open-source text-entry system based on arithmetic coding.
    [ INFORMATION THEORY ] 

ARITHMETICO-GEOMETRIC SERIES

1. Death and statistics
   Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
    [ FINANCIAL MATHEMATICS ] 


2. Mathematical mysteries: The Solitaire Advance
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 

ARITHMETIC SERIES

1. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ] 

ARROW'S THEOREM

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Adam Smith and the invisible hand
   Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
    [ FINANCIAL MATHEMATICS ] 

ARROW PARADOX

1. Mathematical mysteries: Zeno's Paradoxes
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 

ARTHUR C CLARKE

1. A whirlpool of numbers
   The Riemann Hypothesis is probably the hardest unsolved problem in all of mathematics, and one of the most important. It has to do with prime numbers - the building blocks of arithmetic. Nick Mee, together with Sir Arthur C. Clarke, tells us about the patterns hiding inside numbers.
    [ NUMBER THEORY ] 

ARTIFICIAL INTELLIGENCE

1. What computers can't do
   Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
    [ COMPUTER SCIENCE ] 


2. Roger Penrose: A Knight on the tiles
   Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
    [ THEORETICAL PHYSICS ] 


3. CAPTCHA if they can
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


4. A bright idea
   What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
    [ LOGIC ] 

ASTEROID

1. All about asteroids
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


2. Flyby asteroid
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

ASTEROID COLLISION

1. All about asteroids
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


2. Flyby asteroid
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


3. Near miss or normal?
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

ASTRONOMY

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Worldly wobbles
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


3. Career interview: Science communicator
   Science writer and exhibition researcher Alison Boyle tells Plus about her work creating up-to-the-minute news exhibits at the Science Museum in London.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. Nobel mathematics
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 


6. The right spin: how to fly a broken space craft
   On the 25th of May 1997 a dramatic collision tore a hole into the space station Mir and sent it hurtling through space. As NASA astronaut Michael Foale tells Plus, the fate of Mir and its crew hinged on a classical set of equations.
    [ ASTRONOMY ] 


7. Flyby asteroid
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


8. The Nature of Space and Time: An Evening of Speculation
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


9. How not to catch a sunbeam
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 


10. Just a second
    Plus Online Maths Magazine: News Story
     [ ASTRONOMY ] 

ASTROSEISMOLOGY

1. Stellar heartbeats
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

ATIYAH-SINGER INDEX THEOREM

1. Count-abel even if not solve-abel
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

ATTENTIVE USER INTERFACES

1. Is now a good time?
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

ATTRACTOR

1. Robots can't play tennis - yet
   Plus Online Maths Magazine: News Story
    [ CHAOS THEORY ] 

AVAILABILITY ERROR

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

AVALANCHE

1. Career interview: Avalanche researcher
   Jim McElwaine tells Plus how he combines his two loves - mathematics and mountaineering - in avalanche research.
    [ FLUID MECHANICS ] 

AVERAGE

1. Howzat!
   Numbers are bandied around all the time in sports coverage - and cricket is particularly rich in statistics and rankings. It has probably not escaped your attention that the World Cup of cricket has just finished in South Africa (Australia won - again) and so to mark the occasion, Rob Eastaway tells Plus what it takes to be the best.
    [ MATHEMATICAL MODELLING ] 


2. All about averages
   Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.
    [ STATISTICS ] 


3. Damn lies
   Plus Online Maths Magazine: Feature Article
    [ STATISTICS ] 

AXIOM

1. The origins of proof
   Starting in this issue, PASS Maths is pleased to present a series of articles about proof and logical reasoning. In this article we give a brief introduction to deductive reasoning and take a look at one of the earliest known examples of mathematical proof.
    [ LOGIC ] 


2. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 


3. The origins of proof IV: The philosophy of proof
   Robert Hunt concludes our Origins of Proof series by asking what a proof really is, and how we know that we've actually found one. One for the philosophers to ponder...
    [ LOGIC ] 


4. We must know, we will know
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

Back to the top

B

BABBAGE'S ENGINES

1. Prehistoric printer
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


2. Why Was The Computer Invented When It Was?
   Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
    [ COMPUTER SCIENCE ] 

BABY'S ARITHMETICAL EXPECTATIONS

1. Natural born mathematicians
   Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
    [ MATHEMATICAL THINKING ] 

BACKGAMMON

1. Backgammon, doubling the stakes, and Brownian motion
   Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
    [ PROBABILITY ] 

BANACH-TARSKI PARADOX

1. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

BANDWIDTH

1. Bigger bandwidth
   Plus Online Maths Magazine: News Story
    [ INFORMATION THEORY ] 

BANDWIDTH THEOREM

1. Faster than light
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

BARBER'S PARADOX

1. Mathematical mysteries: The Barber's Paradox
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 

BARCODE

1. Take a break
   There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.
    [ CODES ] 

BAYESIAN MODEL

1. Is now a good time?
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

BAYES THEOREM

1. Image analysis - a modern application of mathematics
   New technology has provided us with some amazing images - satellite images, medical images, even images beamed back from Mars. Julian Stander tells us about the increasing role of statistics in interpreting them.
    [ STATISTICS ] 


2. Ye banks and Bayes
   Plus Online Maths Magazine: News Story
    [ FINANCIAL MATHEMATICS ] 


3. Prize specimens
   Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.
    [ COMPUTER SCIENCE ] 


4. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 


5. Beyond reasonable doubt
   In 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, Plus looks at the case and finds out how courts deal with statistics.
    [ STATISTICS ] 


6. Random privacy
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


7. Thomas Bayes & Mr Zootpooper
   The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? Phil Wilson lets his imagination run riot in this intergalactic application of Bayes' Theorem.
    [ PROBABILITY ] 

BEAGLE 2

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

BENDING STIFFNESS

1. Fashion gets physical
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

BENFORD'S LAW

1. Looking out for number one
   You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. Jon Walthoe explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.
    [ NUMBER THEORY ] 

BERNOULLI

1. Mathematical mysteries:
   Plus Online Maths Magazine: Regular Item
    [ HISTORY OF MATHEMATICS ] 

BERNOULLI EQUATION

1. Daniel Bernoulli and the making of the fluid equation
   Daniel Bernoulli (1700-1782) discovered the relationship between the density of a fluid in a pipe, the speed it is travelling in the pipe and the pressure exerted by the fluid against the walls of the pipe. This is the story of what happened.
    [ FLUID MECHANICS ] 


2. Understanding turbulence
   Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
    [ FLUID MECHANICS ] 


3. Testing Bernoulli: a simple experiment
   Here is an experiment that you can easily do yourself to test Bernoulli's equation. There are also 2 questions and answers.
    [ FLUID MECHANICS ] 


4. Prawn crackers
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

BERNOULLI NUMBER

1. Ada Lovelace - visions of today
   Rachel Thomas looks at the life and work of pioneering woman mathematician Ada Lovelace, who foresaw computer-generated music and graphics, despite living long before the computer era.
    [ COMPUTER SCIENCE ] 

BIAS

1. Coincidence, correlation and chance
   How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? Andrew Stickland finds out that, when it comes to probability, our instincts can lead us seriously astray.
    [ PROBABILITY ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ OPINION POLLS ] 

BIFURCATION

1. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 

BIG BANG

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


2. No place like home for Martin Rees
   Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.
    [ ASTRONOMY ] 


3. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 


4. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


5. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


6. Winning background research
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

BINARY CODE

1. Codes, trees and the prefix property
   Underlying our vast global telecommunications networks are codes: formal schemes for representing information in machine-readable and transmissible formats. Kona Macphee examines the prefix property, one of the important features of a good code.
    [ INFORMATION THEORY ] 


2. RIP Claude Shannon
   Claude Shannon, who died on February 24, was the founder of Information Theory, which is the basis of modern telecommunications. Rachel Thomas looks at Shannon's life and works.
    [ INFORMATION THEORY ] 


3. Omega and why maths has no TOEs
   Kurt Gödel, who would have celebrated his 100th birthday next year, showed in 1931 that the power of maths to explain the world is limited: his famous incompleteness theorem proves mathematically that maths cannot prove everything. Gregory Chaitin explains why he thinks that Gödel's incompleteness theorem is only the tip of the iceberg, and why mathematics is far too complex ever to be described by a single theory.
    [ PROOF ] 

BINARY STAR

1. X-otic X-ray visions
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

BIOFEEDBACK LOOP

1. Millennial wobbles
   Plus Online Maths Magazine: News Story
    [ ENGINEERING ] 

BIOLOGY

1. Maths for the broken-hearted
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 


2. Cat count
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

BIOMATHEMATICS

1. Maths on the brain
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

BIOMECHANICAL ENGINEERING

1. Career interview: Biomechanical engineer
   Jose Munoz explains how engineering can allow you to explore the unknown, from understanding how mechanical structures bend to investigating the way genes affect the shape of embryos.
    [ ENGINEERING ] 

BIOMECHANICS

1. Modelling, step by step
   Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.
    [ BIOMATHEMATICS ] 

BIOMETRICS

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

BIRTHDAY PROBLEM

1. What a coincidence!
   Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.
    [ PROBABILITY ] 


2. The luck of the draw
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 

BLACK-SCHOLES EQUATION

1. Career interview: Financial modelling
   David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
    [ FINANCIAL MATHEMATICS ] 

BLACK HOLE

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


2. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 


3. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


4. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


5. X-otic X-ray visions
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

BLACK SCHOLES

1. Career interview: Project finance consultant
   Nick Crawley had recently set up his own financial consultancy firm in Sydney, Australia, offering advice on large-scale financing deals. He tells Plus about the challenges and rewards of working in an incentive-driven environment.
    [ FINANCIAL MATHEMATICS ] 

BLETCHLEY PARK

1. Cracking codes
   In the first of two articles, Artur Ekert takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 


2. Exploring the Enigma
   During the Second World War, the Allies' codebreakers worked at Bletchley Park to decipher the supposedly unbreakable Enigma code. Claire Ellis tells us about their heroic efforts, which historians believe shortened the war by two years.
    [ CRYPTOGRAPHY ] 

BOOLEAN ALGEBRA

1. RIP Claude Shannon
   Claude Shannon, who died on February 24, was the founder of Information Theory, which is the basis of modern telecommunications. Rachel Thomas looks at Shannon's life and works.
    [ INFORMATION THEORY ] 


2. A bright idea
   What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
    [ LOGIC ] 

BOOMERANG

1. Bang up a boomerang!
   Here's how you can make your own cross-shaped boomerang - and it's safe enough to fly indoors! Hugh rolls up his sleeves and proves that theory isn't everything.
    [ AERODYNAMICS ] 


2. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 

BOTTLE EXPERIMENT

1. Testing Bernoulli: a simple experiment
   Here is an experiment that you can easily do yourself to test Bernoulli's equation. There are also 2 questions and answers.
    [ FLUID MECHANICS ] 

BOX DIMENSION

1. How big is the Milky Way?
   A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.
    [ GEOMETRY ] 

BRIDGES OF KONIGSBERG

1. Maths aMazes
   

   C. J. Budd and C. J. Sangwin show us how to create mazes, and explain why mazes and networks have much in common. In fact the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion and conquest...
    [ TOPOLOGY ] 

BROWNIAN MOTION

1. Modelling nature with fractals
   Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
    [ GEOMETRY ] 


2. Backgammon, doubling the stakes, and Brownian motion
   Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
    [ PROBABILITY ] 


3. Dancing with Einstein
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

BRUN'S CONSTANT

1. Mathematical mysteries: twin primes
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

BUBBLE

1. Probing the pint
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. Prawn crackers
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

BUDGET

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ FINANCIAL MATHEMATICS ] 

BUMBLEBEE PARADOX

1. The buzz on bumblebees
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

BUTTERFLY EFFECT

1. Doing the twist
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Finding order in chaos
   All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
    [ CHAOS THEORY ] 


4. Chaotic crochet
   Plus Online Maths Magazine: News Story
    [ CHAOS THEORY ] 

Back to the top

C

CAESAR CIPHER

1. Cracking codes
   In the first of two articles, Artur Ekert takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 

CAESAR SHIFT CIPHER

1. Safety in numbers
   Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
    [ ENCRYPTION ] 

CALCULATING DIGITS OF PI

1. Pushing back Pi
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

CALCULUS

1. Testing Bernoulli: a simple experiment
   Here is an experiment that you can easily do yourself to test Bernoulli's equation. There are also 2 questions and answers.
    [ FLUID MECHANICS ] 


2. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 


3. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

CALL OPTION

1. Rogue trading?
   The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
    [ FINANCIAL MATHEMATICS ] 

CANTOR'S THEOREM

1. What computers can't do
   Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
    [ COMPUTER SCIENCE ] 

CANTOR DUST

1. How big is the Milky Way?
   A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.
    [ GEOMETRY ] 


2. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

CANTOR SET

1. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

CARBON DATING

1. Radioactive decay and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the second of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses radioactive decay.
    [ PHYSICS ] 

CARDIAC ARREST

1. Maths for the broken-hearted
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

CARDINALITY

1. Natural born mathematicians
   Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
    [ MATHEMATICAL THINKING ] 


2. Counting canines
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL THINKING ] 

CAREERS WITH MATHEMATICS

1. Maths adds up
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


3. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

CATASTROPHE THEORY

1. Fishy business
   'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
    [ BIOMATHEMATICS ] 

CAUCHY SURFACE

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 

CAUSATION

1. Coincidence, correlation and chance
   How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? Andrew Stickland finds out that, when it comes to probability, our instincts can lead us seriously astray.
    [ PROBABILITY ] 

CAVITATION

1. Prawn crackers
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

CELESTIAL MECHANICS

1. Mathematical mysteries: the three body problem
   Plus Online Maths Magazine: Regular Item
    [ ASTRONOMY ] 

CELLULAR AUTOMATA

1. Games, Life and the Game of Life
   When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
    [ GAME THEORY ] 

CENSUS

1. Erasing experimental error
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 

CENTRE OF GRAVITY

1. Hardboiled detectives
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

CENTRIFUGAL FORCE

1. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 

CENTRIPETAL FORCE

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

CERN

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

CHANDLER WOBBLE

1. Worldly wobbles
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

CHANNEL ASSIGNMENT PROBLEM

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 

CHAOS

1. Long range forecast
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 


3. Doing the twist
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


4. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 


5. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 


6. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


7. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

CHARLES BABBAGE

1. Ada Lovelace - visions of today
   Rachel Thomas looks at the life and work of pioneering woman mathematician Ada Lovelace, who foresaw computer-generated music and graphics, despite living long before the computer era.
    [ COMPUTER SCIENCE ] 

CHEMICAL ENGINEERING

1. Career interview: Fluid mechanics researcher
   André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.
    [ FLUID MECHANICS ] 

CHEMISTRY

1. Nobel mathematics
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Burning buried sunshine
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

CHESS

1. Kasparov defeated!
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


2. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 


3. Puzzle page
   Plus Online Maths Magazine: Regular Item
    [ CHESS ] 

CHICKEN

1. Game theory and the Cuban missile crisis
   Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.
    [ GAME THEORY ] 

CHINOOK

1. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 

CHIRALITY

1. Through the looking-glass
   Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.
    [ GROUP THEORY ] 


2. Life as we don't know it
   Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
    [ ASTROBIOLOGY ] 


3. Split reflections
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

CHORD

1. The magical mathematics of music
   According to Shakespeare, music is the food of love. But Jeffrey Rosenthal follows Galileo's observation that the entire universe is written in the language of mathematics - and that includes music.
    [ MATHEMATICS AND THE ARTS ] 

CIPHER

1. Cracking codes, part II
   In the second of two articles, Artur Ekert visits the strange subatomic world and investigates the possibility of unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 

CIRCLE-SQUARING

1. Mathematical mysteries: Transcendental meditation
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 


2. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 

CIRCULAR MOTION

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 


2. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 

CLAY INSTITUTE MILLENNIUM PRIZE PROBLEMS

1. Proof for Poincaré?
   Plus Online Maths Magazine: News Story
    [ TOPOLOGY ] 


2. How maths can make you rich and famous
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. But be warned...these problems are hard. In the first of two articles, Chris Budd explains how to hit the bigtime.
    [ OPTIMISATION ] 


3. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 


4. Mathematical millionaire?
   Plus Online Maths Magazine: News Story
    [ TOPOLOGY ] 


5. Mind the gap
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


6. Code-breakers, doughnuts, and violins
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

CLINICAL TRIAL

1. The best medicine?
   To make hard decisions, you need hard facts. Medical statistics can help us to decide what treatment to look for when we are ill, and to estimate our chances of recovery.
    [ STATISTICS ] 

CLOSED-SOURCE

1. Open wide...
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

CMB

1. Winning background research
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

CODE

1. Coding theory: the first 50 years
   Space probes, like NASA's recent Pathfinder mission to Mars, have radio transmitters of only a few watts, but have to transmit pictures and scientific data across hundreds of millions of miles without the information being completely swamped by noise. Read about how coding theory helps.
    [ INFORMATION THEORY ] 


2. Codes, trees and the prefix property
   Underlying our vast global telecommunications networks are codes: formal schemes for representing information in machine-readable and transmissible formats. Kona Macphee examines the prefix property, one of the important features of a good code.
    [ INFORMATION THEORY ] 


3. Interview: Maths student
   In this issue we talk to maths student Emily Dixon about her university studies, and where maths might take her in the future.
    [ MATHEMATICS EDUCATION ] 


4. Career interview: IT project manager
   Bharat Dodia tells Plus how his love of maths has taken him from turbulent times to building better IT systems for Ford.
    [ MATHEMATICS EDUCATION ] 


5. A mathematical mystery begins...
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

COIN-TOSSING

1. What a coincidence!
   Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.
    [ PROBABILITY ] 

COINCIDENCE

1. What a coincidence!
   Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.
    [ PROBABILITY ] 

COLD WAR

1. Graphical methods I: Slug wars
   To arm or to disarm? This is the question in Phil Wilson's article, which explores the maths behind a cold war in slug world.
    [ GRAPHICAL METHODS ] 


2. Graphical Methods II: The return of the slime
   In last issue's Graphical methods I Phil Wilson used maths to predict the outcome of a cold war in slug world. In this self-contained article he looks at slug world after the disaster: with only a few survivors and all infra-structure destroyed, which species will take root and how will they develop? Graphs can tell it all.
    [ GRAPHICAL METHODS ] 

COLLATZ PROBLEM

1. More hailstones...
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

COLOURING

1. Friends and strangers
   Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.
    [ COMBINATORICS ] 

COMPACT UNIVERSE

1. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 

COMPLEX DYNAMICS

1. Unveiling the Mandelbrot set
   Plus Online Maths Magazine: Feature Article
    [ FRACTAL ] 

COMPLEX NUMBER

1. Roger Penrose: A Knight on the tiles
   Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
    [ THEORETICAL PHYSICS ] 


2. Curious quaternions
   Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the first of two articles, he talks about connections between algebra and geometry, and the importance of lateral thinking in mathematics.
    [ ARITHMETIC ] 


3. Ubiquitous octonions
   Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.
    [ ARITHMETIC ] 


4. Unveiling the Mandelbrot set
   Plus Online Maths Magazine: Feature Article
    [ FRACTAL ] 


5. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 

COMPOUND INTEREST

1. Have we caught your interest?
   Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
    [ FINANCIAL MATHEMATICS ] 


2. Death and statistics
   Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
    [ FINANCIAL MATHEMATICS ] 

COMPUTER ANIMATION

1. Career interview: Games developer
   In the real world, balls bounce and water splashes because of the laws of physics. In computer games, a physics engine ensures the virtual world behaves realistically. Mathematician and computer programmer Nick Gray tells us about playing God in a virtual world.
    [ COMPUTER SCIENCE ] 


2. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 

COMPUTER CHESS

1. Kasparov defeated!
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


2. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 

COMPUTER GAMING

1. Career interview: Games developer
   Andrew Wensley works at Eidos Interactive, the company who publish the mega-successful computer game Tomb Raider, featuring 90s icon Lara Croft. Andrew is a long-term computer game fan with an academic background in maths. PASS Maths caught up with him at Eidos's Wimbledon offices.
    [ COMPUTER SCIENCE ] 


2. Career interview: Games developer
   In the real world, balls bounce and water splashes because of the laws of physics. In computer games, a physics engine ensures the virtual world behaves realistically. Mathematician and computer programmer Nick Gray tells us about playing God in a virtual world.
    [ COMPUTER SCIENCE ] 


3. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 

COMPUTER GRAPHICS

1. Career interview: Games developer
   In the real world, balls bounce and water splashes because of the laws of physics. In computer games, a physics engine ensures the virtual world behaves realistically. Mathematician and computer programmer Nick Gray tells us about playing God in a virtual world.
    [ COMPUTER SCIENCE ] 


2. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


3. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 


4. Virtually reducing the 3D load
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

COMPUTER MARKING

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 

COMPUTER PROGRAMMING

1. What mathematicians get up to
   After 5,000 years, the game of Nine Men's Morris has succumbed to the power of modern computing, plus other recent mathematical discoveries in the world of games.
    [ GAME THEORY ] 


2. Pilgrims, planes and postage stamps
   Practical problems often have no exact mathematical solution, and we have to resort to using unusual techniques to solve them. From navigation in the 17th century to postage stamps, see how this principle applies to a variety of real-life problems - and also learn how to use a piece of string to locate a German bomber!
    [ ENGINEERING ] 


3. Career interview: Financial modelling
   David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
    [ FINANCIAL MATHEMATICS ] 


4. Oops!
   Plus Online Maths Magazine: News Story
    [ ENCRYPTION ] 


5. Beat the crush
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


6. Career interview: Aerodynamicist
   Plus talks to Christine Hogan, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team.
    [ AERODYNAMICS ] 


7. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


8. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 

COMPUTER RECOGNITION

1. Fishy business
   'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
    [ BIOMATHEMATICS ] 

COMPUTER SCIENCE

1. Pushing back Pi
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


2. Career interview: Statistical consulting
   John Henstridge and Jodie Thompson tell Plus about life as consultant statisticians, modelling real-world problems in areas as diverse as the shipping industry and water rationing.
    [ STATISTICS ] 


3. Maths on the brain
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


4. A bright idea
   What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
    [ LOGIC ] 


5. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN THE MEDIA ] 


6. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


7. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


8. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 


9. Forever rich
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


10. Machine prose
    Plus Online Maths Magazine: News Story
     [ COMPUTER SCIENCE ] 

COMPUTER SEARCH

1. Discovering new primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


2. Prize specimens
   Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.
    [ COMPUTER SCIENCE ] 


3. Forever rich
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

COMPUTER SIMULATION

1. Understanding turbulence
   Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
    [ FLUID MECHANICS ] 


2. Call routing in telephone networks
   Find out how modern telephone networks use mathematics to make it possible for a person to dial a friend in another country just as easily as if they were in the same street, or to read web pages that are on a computer in another continent.
    [ INFORMATION THEORY ] 


3. Career interview - Meteorologist
   Read about what it is like to work at the Meteorological Office in this interview with Helen Hewson. There's also a contact point for careers information.
    [ FLUID MECHANICS ] 


4. Monte Carlo Monopoly
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


5. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


6. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


7. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 

CONDITIONAL PROBABILITY

1. Ye banks and Bayes
   Plus Online Maths Magazine: News Story
    [ FINANCIAL MATHEMATICS ] 


2. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 


3. Beyond reasonable doubt
   In 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, Plus looks at the case and finds out how courts deal with statistics.
    [ STATISTICS ] 


4. The best medicine?
   To make hard decisions, you need hard facts. Medical statistics can help us to decide what treatment to look for when we are ill, and to estimate our chances of recovery.
    [ STATISTICS ] 


5. Thomas Bayes & Mr Zootpooper
   The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? Phil Wilson lets his imagination run riot in this intergalactic application of Bayes' Theorem.
    [ PROBABILITY ] 

CONGRUENCE

1. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 

CONIC SECTIONS

1. Drinking coffee in the Klein Café
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 

CONNECTEDNESS

1. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 

CONSERVATION OF ANGULAR MOMENTUM

1. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 

CONTINUED FRACTION

1. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 

CONTINUITY

1. The origins of fractals
   The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.
    [ GEOMETRY ] 

CONTRACT

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 


2. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 

CONTRAST

1. Let there be light... (but not too much!)
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

CONVERGENCE

1. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 


2. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ]   [ ARITHMETIC ] 


3. Mathematical mysteries: Zeno's Paradoxes
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 


4. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 

COOPERATION

1. Mathematical mysteries: Survival of the nicest?
   Plus Online Maths Magazine: Regular Item
    [ GAME THEORY ] 

COPERNICUS

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

CORIOLIS FORCE

1. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 

CORRELATION

1. Coincidence, correlation and chance
   How much evidence would you need before buying into a get rich quick scheme? Do high ice cream sales cause shark attacks? And just how likely was it that you were ever born? Andrew Stickland finds out that, when it comes to probability, our instincts can lead us seriously astray.
    [ PROBABILITY ] 


2. All about averages
   Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.
    [ STATISTICS ] 

COSINE

1. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 

COSMIC BACKGROUND RADIATION

1. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 

COSMIC CENSORSHIP

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 

COSMIC MICROWAVE BACKGROUND RADIATION

1. Winning background research
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

COSMOLOGICAL INFLATION

1. The search for Higgs
   Plus Online Maths Magazine: News Story
    [ PARTICLE PHYSICS ] 


2. New light shed on dark energy
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

COSMOLOGY

1. Cosmos launch
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


2. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 


3. Lensing helps see in the dark
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


4. The search for Higgs
   Plus Online Maths Magazine: News Story
    [ PARTICLE PHYSICS ] 


5. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


6. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


7. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


8. Faster than a falling bullet...
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


9. New light shed on dark energy
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


10. Building Newton's nest
    Plus Online Maths Magazine: News Story
     [ PHYSICS ] 


11. Winning background research
    Plus Online Maths Magazine: News Story
     [ PHYSICS ] 

COUPLE

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 

CROSSING

1. Why knot: knots, molecules and stick numbers
   Knots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?
    [ TOPOLOGY ] 

CROWD DYNAMICS

1. Beat the crush
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

CRYPTOGRAPHY

1. Terrorists' code of honour
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


2. Safety in numbers
   Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
    [ ENCRYPTION ] 


3. A whirlpool of numbers
   The Riemann Hypothesis is probably the hardest unsolved problem in all of mathematics, and one of the most important. It has to do with prime numbers - the building blocks of arithmetic. Nick Mee, together with Sir Arthur C. Clarke, tells us about the patterns hiding inside numbers.
    [ NUMBER THEORY ] 


4. Calling all code crackers
   Plus Online Maths Magazine: News Story
    [ CODES ] 


5. A mathematical mystery begins...
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

CUBIC EQUATIONS

1. Mathematical Mysteries: Trisecting the Angle
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 

CURRENT

1. A current problem
   Frances Elwell looks at the eddies and currents, from the pungent problem of sewage outflow to the search for bodies of people who have fallen into rivers, explaining that fluid mechanics lies behind it all.
    [ FLUID MECHANICS ] 

CURVATURE

1. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 


2. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


3. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

CURVATURE OF SPACE

1. No place like home for Martin Rees
   Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.
    [ ASTRONOMY ] 


2. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 


3. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


4. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


5. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 

CUT-AND-SHIFT PROOF

1. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 

Back to the top

D

DAMPING

1. Just a little turbulence
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

DANCE

1. Dancing with Einstein
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

DARK ENERGY

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

DARK MATTER

1. Lensing helps see in the dark
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


2. No place like home for Martin Rees
   Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.
    [ ASTRONOMY ] 


3. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

DATA ANALYSIS

1. Random privacy
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


2. Travel-time maps — transforming our view of transport
   Plus Online Maths Magazine: News Story
    [ VISUALISATION ] 

DATABASE

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

DATA COMPRESSION

1. Text, Bytes and Videotape
   How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.
    [ INFORMATION THEORY ] 

DATA HANDLING

1. Erasing experimental error
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 


2. Travel-time maps — transforming our view of transport
   Plus Online Maths Magazine: News Story
    [ VISUALISATION ] 

DATAMINING

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

DATA SAMPLING

1. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 

DAVID GREGORY

1. Newton and the kissing problem
   In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
    [ GEOMETRY ] 

DE BROGLIE RELATION

1. Quantum uncertainty
   Quantum mechanics is the physics of the extremely small. With something so far outside our everyday experience it's not surprising to find mathematics at the heart of it all. But at the quantum scale nothing in life is certain... Peter Landshoff explains.
    [ QUANTUM MECHANICS ] 

DECISION THEORY

1. Dynamic programming: an introduction
   The previous feature, "Mathematics, marriage and finding somewhere to eat" investigated the problem of finding the best potential partner from a fixed number of potential partners using a technique known as "optimal stopping". Inevitably, mathematicians and mathematical psychologists have constructed other models of the problem...
    [ INFORMATION THEORY ] 


2. Mathematics, marriage and finding somewhere to eat
   How do you choose a partner? Is it an irrational choice or is it made rationally, based on a mathematical model which analyses the best potential partner you are likely to meet?
    [ PROBABILITY ] 


3. Opinion
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

DECLINATION OF THE SUN

1. Analemmatic sundials: How to build one and why they work
   We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.
    [ GEOMETRY ] 

DEDUCTION

1. The origins of proof
   Starting in this issue, PASS Maths is pleased to present a series of articles about proof and logical reasoning. In this article we give a brief introduction to deductive reasoning and take a look at one of the earliest known examples of mathematical proof.
    [ LOGIC ] 


2. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 

DEEP BLUE

1. Kasparov defeated!
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


2. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 

DEGREE OF FIT

1. Maths in the dock
   Chemists John Watling and Allen Thomas talk to Plus about the vital role of maths in presenting criminal evidence.
    [ STATISTICS ] 

DERANGEMENT

1. Puzzle page
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

DERIVATIVE INSTRUMENT

1. Career interview: Financial modelling
   David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
    [ FINANCIAL MATHEMATICS ] 


2. Rogue trading?
   The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
    [ FINANCIAL MATHEMATICS ] 

DES

1. Safety in numbers
   Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
    [ ENCRYPTION ] 

DESIGN

1. Career interview: furniture design
   Two designers tell us how they took the long way round to design, and how the maths and science they took in on the way helps them with their work today.
    [ MATHEMATICS AND THE ARTS ] 

DIAGONALISATION ARGUMENT

1. What computers can't do
   Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
    [ COMPUTER SCIENCE ] 

DIAGONAL SYMMETRY

1. New designs from Africa
   Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
    [ GEOMETRY ] 

DICE

1. Let 'em roll
   Plus Online Maths Magazine: Feature Article
    [ PROBABILITY ] 

DIFFERENCE ENGINE

1. Ada Lovelace - visions of today
   Rachel Thomas looks at the life and work of pioneering woman mathematician Ada Lovelace, who foresaw computer-generated music and graphics, despite living long before the computer era.
    [ COMPUTER SCIENCE ] 

DIFFERENTIABILITY

1. The origins of fractals
   The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.
    [ GEOMETRY ] 

DIFFERENTIAL EQUATION

1. Career interview - Meteorologist
   Read about what it is like to work at the Meteorological Office in this interview with Helen Hewson. There's also a contact point for careers information.
    [ FLUID MECHANICS ] 


2. Natural frequencies and music
   In the first of two articles, David Henwood discusses the vibrations that can be harnessed by musical instrument makers.
    [ PHYSICS ] 


3. The mathematics of diseases
   Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic infection parameters. Matthew Keeling describes some of the mathematical developments that have improved our understanding and predictive ability.
    [ MATHEMATICAL MODELLING ] 


4. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. Chaos in the brain
   Saying that someone is a chaotic thinker might seems like an insult - but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.
    [ CHAOS THEORY ] 


6. A differential story
   Plus Online Maths Magazine: News Story
    [ ABEL PRIZE ] 

DIFFERENTIAL EQUATIONS

1. Career interview: Financial maths course director
   Riaz Ahmad's mathematical career has led him from the complexities of blood flow to the risks of the financial markets via underwater acoustics. Plus found out how maths can explain all this and more.
    [ FINANCIAL MATHEMATICS ] 

DIFFRACTION

1. Light's identity crisis
   What is light? Sometimes it seems wave-like and sometimes particle like. See how Einstein applied his theory of relativity to the problem, predicted that photons have no mass and laid the foundations for quantum mechanics.
    [ QUANTUM MECHANICS ] 

DIFFUSION

1. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 


2. How the leopard got its spots
   How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Lewis Dartnell solves these, and other, puzzles of animal patterning.
    [ DIFFERENTIAL EQUATIONS ] 

DIGITAL PHOTOGRAPHY

1. Let there be light... (but not too much!)
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

DIGITAL SIGNAL PROCESSING

1. Career interview: Audio software engineer
   Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
    [ FOURIER ANALYSIS ] 


2. And the Oscar goes to...
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

DIMENSION

1. Jackson's fractals
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


2. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 


3. How big is the Milky Way?
   A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.
    [ GEOMETRY ] 

DIMENSIONLESS GROUPS

1. Model behaviour
   To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
    [ MATHEMATICAL MODELLING ] 

DIOPHANTINE EQUATION

1. Woman joins Adams family
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

DIRAC'S EQUATION

1. Dirac Centennial
   Plus Online Maths Magazine: News Story
    [ QUANTUM MECHANICS ] 


2. In a spin
   When it comes to the science of the very small, strange things start happening, and our intuition ceases to be a useful guide. Plus finds out about the crazy quantum world, and spin that a politician would die for.
    [ PARTICLE PHYSICS ] 

DISPERSION

1. Faster than light
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

DISSECTION PROOF

1. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 

DISTORTION

1. Designing loudspeakers
   In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.
    [ PHYSICS ] 

DISTRIBUTED COMPUTING

1. Career interview: Aerodynamicist
   Plus talks to Christine Hogan, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team.
    [ AERODYNAMICS ] 


2. Charity begins @home
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


3. New largest prime discovered!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


4. Help defeat malaria in Africa
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


5. Volunteers discover new largest prime
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

DISTRIBUTION OF DIGITS

1. Looking out for number one
   You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. Jon Walthoe explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.
    [ NUMBER THEORY ] 

DIVERGENCE

1. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ] 


2. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 

DNA

1. Understanding the noise
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 


2. Clever coiling
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

DNA EVIDENCE

1. Seeking truth with statistics
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

DOMINATED STRATEGY

1. Blast it like Beckham?
   What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.
    [ GAME THEORY ] 

DOPPLER SHIFT

1. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 


2. Stellar heartbeats
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


3. Brave young worlds
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


4. Flyby asteroid
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


5. Doppler detectives
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

DOUBLE PENDULUM

1. Finding order in chaos
   All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
    [ CHAOS THEORY ] 

DOUBLING CUBE

1. Backgammon, doubling the stakes, and Brownian motion
   Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
    [ PROBABILITY ] 


2. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 

DOUBLING STRATEGY

1. Backgammon, doubling the stakes, and Brownian motion
   Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
    [ PROBABILITY ] 

DRAG

1. Probing the pint
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

DRAPING

1. Fashion gets physical
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

DRAUGHTS

1. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 

DYNAMICAL SYSTEM

1. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 


2. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 


4. Vaccination works
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 


5. A fat chance of chaos?
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 

DYNAMICAL SYSTEMS

1. Abel to iPod
   Plus Online Maths Magazine: News Story
    [ ABEL PRIZE ] 

DYNAMIC PROGRAMMING

1. Dynamic programming: an introduction
   The previous feature, "Mathematics, marriage and finding somewhere to eat" investigated the problem of finding the best potential partner from a fixed number of potential partners using a technique known as "optimal stopping". Inevitably, mathematicians and mathematical psychologists have constructed other models of the problem...
    [ INFORMATION THEORY ] 

DYNAMO EFFECT

1. Core business
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. Untangling a magnetic mystery
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

DYSLEXIA

1. Career interview: Systems administrator
   Steve Traylen tells Plus about life as a Systems Administrator.
    [ COMPUTER SCIENCE ] 

DYSPRAXIA

1. Natural born mathematicians
   Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
    [ MATHEMATICAL THINKING ] 

Back to the top

E

E

1. Mathematical mysteries: Transcendental meditation
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

EARTHQUAKE

1. Quake-proof
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

ECLIPSE

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Planets, planets everywhere
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

ECONOMIC PREDICTION

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ FINANCIAL MATHEMATICS ] 


2. Graphical methods III: the slugs bounce back
   Plus Online Maths Magazine: Feature Article
    [ GRAPHICAL METHODS ] 

ECONOMICS

1. Nobel mathematics
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Career interview: Financial maths course director
   Riaz Ahmad's mathematical career has led him from the complexities of blood flow to the risks of the financial markets via underwater acoustics. Plus found out how maths can explain all this and more.
    [ FINANCIAL MATHEMATICS ] 


3. Graphical methods III: the slugs bounce back
   Plus Online Maths Magazine: Feature Article
    [ GRAPHICAL METHODS ] 


4. Career interview: Business analyst
   From Einstein to water power, Plus author Anita King explains where maths has got her.
    [ BUSINESS ANALYSIS ] 


5. How to measure a million
   Plus Online Maths Magazine: News Story
    [ ECONOMICS ] 


6. Winning background research
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

EDDIES

1. A current problem
   Frances Elwell looks at the eddies and currents, from the pungent problem of sewage outflow to the search for bodies of people who have fallen into rivers, explaining that fluid mechanics lies behind it all.
    [ FLUID MECHANICS ] 

EFFICIENT CODING

1. Text, Bytes and Videotape
   How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.
    [ INFORMATION THEORY ] 

EFRON'S DICE

1. Let 'em roll
   Plus Online Maths Magazine: Feature Article
    [ PROBABILITY ] 

EINSTEIN

1. Dancing with Einstein
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. What's so special about special relativity?
   Most of us are aware that Einstein proved that everything was relative ... or something like that. But we go no further, believing that we aren't clever enough to understand what he did. Hardeep Aiden sets out to persuade readers that they too can understand an idea as elegantly simple as it was original.
    [ SPECIAL RELATIVITY, ] 


4. Einstein as icon
   One hundred years ago, in 1905, Albert Einstein changed physics forever with his special theory of relativity. Since then his name — and hair do — have become synonymous with genius. John D Barrow looks at Einstein as a media star.
    [ MATHEMATICS IN THE MEDIA ] 


5. New light shed on dark energy
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


6. Spinning in space
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

EINSTEIN YEAR

1. Dancing with Einstein
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

ELECTION

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ OPINION POLLS ] 

ELECTRIC FIELD

1. Bigger bandwidth
   Plus Online Maths Magazine: News Story
    [ INFORMATION THEORY ] 

ELECTROMAGNETISM

1. Light's identity crisis
   What is light? Sometimes it seems wave-like and sometimes particle like. See how Einstein applied his theory of relativity to the problem, predicted that photons have no mass and laid the foundations for quantum mechanics.
    [ QUANTUM MECHANICS ] 


2. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 


3. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


4. Symmetry rules
   Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how not only shapes, but also laws of nature can be symmetrical, and how this aids our understanding of the universe.
    [ SYMMETRY ] 

ELECTRONICS

1. Career interview - Electronic engineer
   Geraldine Paxton, an electronics engineer, is a member of the Ford Motor Company Limited's graduate trainee scheme. Geraldine tells us about her work there, from driving cars on the German autobahns to ensuring production lines keep working. There's also salary information and a careers contact point.
    [ ENGINEERING ] 


2. Career interview: Theoretical Physics Researcher
   Francesco Mezzadri from Italy and Nina Snaith from Canada are PhD students in Applied Mathematics at the University of Bristol. They are also affiliated with Hewlett Packard's BRIMS Laboratory. PASS Maths went to visit them there.
    [ THEORETICAL PHYSICS ] 

ELECTRON SPIN

1. In a spin
   When it comes to the science of the very small, strange things start happening, and our intuition ceases to be a useful guide. Plus finds out about the crazy quantum world, and spin that a politician would die for.
    [ PARTICLE PHYSICS ] 

ELLIPSE

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Analemmatic sundials: How to build one and why they work
   We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.
    [ GEOMETRY ] 


3. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 


4. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

ELLIPTIC CURVE

1. Woman joins Adams family
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

ELLIPTIC GEOMETRY

1. Still life
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

EMERGENT BEHAVIOUR

1. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 

EMMY NOETHER

1. Against the odds
   Danielle Stretch looks back at the remarkable life of pioneering mathematician Emmy Amalie Noether (1882-1935). Despite her constant struggles to make her way in a man's world, she made significant contributions to the development of modern algebra.
    [ HISTORY OF MATHEMATICS ] 

ENCRYPTION

1. Terrorists' code of honour
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

ENDANGERED SPECIES

1. Reflecting on extinction
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

ENERGY

1. Light's identity crisis
   What is light? Sometimes it seems wave-like and sometimes particle like. See how Einstein applied his theory of relativity to the problem, predicted that photons have no mass and laid the foundations for quantum mechanics.
    [ QUANTUM MECHANICS ] 


2. Old problem, new spin
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


3. No place like home for Martin Rees
   Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.
    [ ASTRONOMY ] 


4. Folding under pressure
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


5. In skimming, spin's the thing
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


6. Burning buried sunshine
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

ENGINEERING

1. Outer space: Bridging that gap
   Plus Online Maths Magazine: Regular Item
    [ ENGINEERING ] 


2. Quake-proof
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


3. Bracing for the storm
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ENVIRONMENT ] 

ENIGMA

1. Cracking codes
   In the first of two articles, Artur Ekert takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 


2. Exploring the Enigma
   During the Second World War, the Allies' codebreakers worked at Bletchley Park to decipher the supposedly unbreakable Enigma code. Claire Ellis tells us about their heroic efforts, which historians believe shortened the war by two years.
    [ CRYPTOGRAPHY ] 

ENTROPY

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


2. Text, Bytes and Videotape
   How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.
    [ INFORMATION THEORY ] 

EPIDEMIOLOGY

1. The mathematics of diseases
   Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic infection parameters. Matthew Keeling describes some of the mathematical developments that have improved our understanding and predictive ability.
    [ MATHEMATICAL MODELLING ] 


2. Anticipating anthrax
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


3. Model behaviour
   To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
    [ MATHEMATICAL MODELLING ] 


4. Understanding influenza
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

EQUATION OF STATE

1. X-otic X-ray visions
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

EQUILIBRIUM

1. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 


2. Love's a gamble
   Plus Online Maths Magazine: News Story
    [ GAME THEORY ] 

ERLANG'S FORMULA

1. Call routing in telephone networks
   Find out how modern telephone networks use mathematics to make it possible for a person to dial a friend in another country just as easily as if they were in the same street, or to read web pages that are on a computer in another continent.
    [ INFORMATION THEORY ] 


2. Agner Krarup Erlang (1878 - 1929)
   The mathematics underlying today's complex telephone networks is still based on his work. Erlang was the first person to study the problem of telephone networks.
    [ HISTORY OF MATHEMATICS ] 

ERROR

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 

ERROR-CORRECTING CODE

1. Coding theory: the first 50 years
   Space probes, like NASA's recent Pathfinder mission to Mars, have radio transmitters of only a few watts, but have to transmit pictures and scientific data across hundreds of millions of miles without the information being completely swamped by noise. Read about how coding theory helps.
    [ INFORMATION THEORY ] 


2. Take a break
   There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.
    [ CODES ] 


3. Mathematical mysteries: What colour is my hat?
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 

ESA

1. Brave young worlds
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

ESCHER

1. From quasicrystals to Kleenex
   This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.
    [ GEOMETRY ] 


2. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


3. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


4. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

ESTIMATION

1. Cars in the next lane really do go faster
   Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
    [ STATISTICS ] 

ETERNITY GAME

1. Prize specimens
   Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.
    [ COMPUTER SCIENCE ] 


2. Forever rich
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

ETHICS OF SCIENCE

1. A conversation with Freeman Dyson
   The 2003 Dirac Lecturer, distinguished physicist Freeman Dyson, tells Plus why he is an optimist, what makes life interesting and why old-fashioned maths is what you need for physics.
    [ THEORETICAL PHYSICS ] 

EUCLID'S ALGORITHM

1. Music and Euclid's algorithm
   Plus Online Maths Magazine: Feature Article
    [ MATHEMATICS AND THE ARTS ] 

EUCLID'S ELEMENTS

1. The origins of proof
   Starting in this issue, PASS Maths is pleased to present a series of articles about proof and logical reasoning. In this article we give a brief introduction to deductive reasoning and take a look at one of the earliest known examples of mathematical proof.
    [ LOGIC ] 


2. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 

EUCLIDEAN GEOMETRY

1. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


2. We must know, we will know
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

EULER

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 


2. "Read Euler, read Euler, he is the master of us all."
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

EULER'S DISK

1. Old problem, new spin
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

EULER'S SOLUTION TO THE BASEL PROBLEM

1. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 

EULER YEAR

1. "Read Euler, read Euler, he is the master of us all."
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

EUROPEAN SPACE AGENCY

1. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 

EVARISTE GALOIS

1. Genius, stupidity and genius again
   Tope Omitola looks back at the tragically short but inspiringly productive life of a true original: Evariste Galois.
    [ HISTORY OF MATHEMATICS ] 

EVOLUTION

1. Mathematical mysteries: Survival of the nicest?
   Plus Online Maths Magazine: Regular Item
    [ GAME THEORY ] 


2. Understanding influenza
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


3. Life as we don't know it
   Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
    [ ASTROBIOLOGY ] 

EXAMINATIONS

1. Career interview - Qualifications Manager
   Karen Reid, whose hobbies include badminton and salsa dancing, is a Maths graduate. She works as a Qualifications Manager at RSA Examinations Board, Coventry and has also taught Maths.
    [ MANAGEMENT ] 


2. Editorial
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


3. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. Opinion
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


6. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 

EXPECTED PRIZE

1. Mathematical mysteries:
   Plus Online Maths Magazine: Regular Item
    [ HISTORY OF MATHEMATICS ] 

EXPONENTIAL LAW

1. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 


2. Radioactive decay and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the second of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses radioactive decay.
    [ PHYSICS ] 

EXPONENTIALLY DECAYING AVERAGE

1. Howzat!
   Numbers are bandied around all the time in sports coverage - and cricket is particularly rich in statistics and rankings. It has probably not escaped your attention that the World Cup of cricket has just finished in South Africa (Australia won - again) and so to mark the occasion, Rob Eastaway tells Plus what it takes to be the best.
    [ MATHEMATICAL MODELLING ] 

Back to the top

F

FAIR DIVISION

1. Better ways to cut a cake
   Plus Online Maths Magazine: News Story
    [ OPTIMISATION ] 

FASHION

1. Fashion gets physical
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

FERMAT'S LAST THEOREM

1. The origins of proof IV: The philosophy of proof
   Robert Hunt concludes our Origins of Proof series by asking what a proof really is, and how we know that we've actually found one. One for the philosophers to ponder...
    [ LOGIC ] 


2. Woman joins Adams family
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


3. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 


4. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 


5. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN THE MEDIA ] 


6. Another proof for Fermat's last theorem
   Plus Online Maths Magazine: News Story
    [ FERMAT'S LAST THEOREM ] 

FIBONACCI NUMBER

1. The life and numbers of Fibonacci
   Fibonacci, famous for the Fibonacci sequence, also introduced the decimal system into Europe.
    [ NUMBER THEORY ] 


2. A postcard from Italy
   Eugen Jost is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.
    [ MATHEMATICS AND THE ARTS ] 


3. Self-similar syncopations:
   Fibonacci, L-systems, limericks and ragtime
   Kevin Jones investigates the links between music and mathematics, throwing in limericks, Fibonacci and Scott Joplin along the way. Plus is proud to present an extended version of his winning entry for the THES/OUP 1999 Science Writing Prize.
    [ MATHEMATICS AND THE ARTS ] 


4. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. The golden ratio and aesthetics
   It was Euclid who first defined the Golden Ratio, and ever since people have been fascinated by its extraordinary properties. Find out if beauty is in the eye of the beholder, and how the Golden Ratio crosses from mathematics to the arts.
    [ MATHEMATICS AND THE ARTS ] 

FIELDS MEDAL

1. Fields medals
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. And the winner is ...
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. A Fields of their own
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. En-Abeled
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. Mathematical millionaire?
   Plus Online Maths Magazine: News Story
    [ TOPOLOGY ] 


6. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN THE MEDIA ] 


7. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN THE MEDIA ] 


8. The Fields Medals 2006
   Plus Online Maths Magazine: News Story
    [ FIELDS MEDAL ] 

FILM INDUSTRY

1. Career interview: Film marketing analyst
   Francesca Harris has always known she wanted to work in the music or film industry, and she has found that her maths skills have stood her in good stead as she works her way up.
    [ MARKETING ] 

FINANCIAL MATHEMATICS

1. Career interview: Financial maths course director
   Riaz Ahmad's mathematical career has led him from the complexities of blood flow to the risks of the financial markets via underwater acoustics. Plus found out how maths can explain all this and more.
    [ FINANCIAL MATHEMATICS ] 

FINITE ELEMENTS

1. Designing loudspeakers
   In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.
    [ PHYSICS ] 

FLATNESS

1. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 

FLUID MECHANICS

1. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 


3. Untangling a magnetic mystery
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


4. Eye on the ball
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN SPORT ] 


5. And now, the weather...
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


6. When will they blow?
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

FM (FREQUENCY MODULATION)

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 

FOCAL POINTS

1. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

FOLDING

1. Fashion gets physical
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

FOOD ENGINEERING

1. Fuzzy pizza
   Plus Online Maths Magazine: News Story
    [ ENGINEERING ] 


2. GM trials come a cropper
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

FOOTBALL

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN SPORT ] 


2. The luck of the draw
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


3. Eye on the ball
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN SPORT ] 

FOOTBALL STRATEGY

1. On the ball
   If your team scores first in a football match, how likely is it to win? And when is it worth committing a professional foul? John Haigh shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.
    [ GAME THEORY ] 


2. Blast it like Beckham?
   What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.
    [ GAME THEORY ] 

FORCE

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 


2. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 


3. Folding under pressure
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

FORECASTING

1. Long range forecast
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 


3. And now, the weather...
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

FORENSIC MATHEMATICS

1. Maths in the dock
   Chemists John Watling and Allen Thomas talk to Plus about the vital role of maths in presenting criminal evidence.
    [ STATISTICS ] 

FORMULA FOR PI

1. Pi not a piece of cake
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

FORWARD CONTRACT

1. Rogue trading?
   The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
    [ FINANCIAL MATHEMATICS ] 

FOSSIL FUELS

1. Burning buried sunshine
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

FOUCAULT'S PENDULUM

1. Mathematical mysteries: Foucault's pendulum and the eclipse
   Plus Online Maths Magazine: Regular Item
    [ PHYSICS ] 

FOUNDATIONS OF MATHEMATICS

1. Mathematical mysteries: The Barber's Paradox
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 

FOUR-COLOUR THEOREM

1. The origins of proof IV: The philosophy of proof
   Robert Hunt concludes our Origins of Proof series by asking what a proof really is, and how we know that we've actually found one. One for the philosophers to ponder...
    [ LOGIC ] 


2. Helping business make a crust
   Plus Online Maths Magazine: News Story
    [ INDUSTRIAL MATHEMATICS ] 

FOURIER ANALYSIS

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


2. Career interview: Systems administrator
   Steve Traylen tells Plus about life as a Systems Administrator.
    [ COMPUTER SCIENCE ] 


3. Career interview: Audio software engineer
   Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
    [ FOURIER ANALYSIS ] 


4. Career interview: computer music researcher
   Teaching a machine to understand music is an incredibly difficult task, which uses all the mathematical power of digital signal processing. But teaching a machine to compose music is quite another matter, and the wonderful world of mathematical patterns proves to be a gold mine. Nick Collins talks to Plus about his artifical musician.
    [ MATHEMATICS AND THE ARTS ] 


5. And the Oscar goes to...
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 


6. Abel to iPod
   Plus Online Maths Magazine: News Story
    [ ABEL PRIZE ] 


7. Forget Sudoku and smile for the camera
   Plus Online Maths Magazine: News Story
    [ IMAGE ANALYSIS ] 

FRACTAL

1. The origins of fractals
   The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.
    [ GEOMETRY ] 


2. Modelling nature with fractals
   Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
    [ GEOMETRY ] 


3. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 


4. Jackson's fractals
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


5. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 


6. How big is the Milky Way?
   A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.
    [ GEOMETRY ] 


7. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 


8. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 


9. Outer space: Superficiality
   Plus Online Maths Magazine: Regular Item
    [ FRACTAL ] 


10. Unveiling the Mandelbrot set
    Plus Online Maths Magazine: Feature Article
     [ FRACTAL ] 


11. Vaccination works
    Plus Online Maths Magazine: News Story
     [ DYNAMICAL SYSTEM ] 


12. A fat chance of chaos?
    Plus Online Maths Magazine: News Story
     [ DYNAMICAL SYSTEM ] 


13. The artist's fractal fingerprint
    Plus Online Maths Magazine: News Story
     [ FRACTAL ] 


14. Bridges: mathematical connections in art and music
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS AND THE ARTS ] 

FRACTAL FORGERY

1. Modelling nature with fractals
   Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
    [ GEOMETRY ] 

FRAUD DETECTION

1. Looking out for number one
   You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. Jon Walthoe explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.
    [ NUMBER THEORY ] 

FREEMAN DYSON

1. A conversation with Freeman Dyson
   The 2003 Dirac Lecturer, distinguished physicist Freeman Dyson, tells Plus why he is an optimist, what makes life interesting and why old-fashioned maths is what you need for physics.
    [ THEORETICAL PHYSICS ] 

FREE MARKET

1. Adam Smith and the invisible hand
   Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
    [ FINANCIAL MATHEMATICS ] 

FREQUENCY

1. Decoding a war time diary
   An account of how a prisoner of war's diary was recently decoded. Donald Hill wrote his diary in a numerical code, disguised as a set of mathematical tables, while in Hong Kong during and after the Japanese invasion of 1941.
    [ ENCRYPTION ] 


2. Natural frequencies and music
   In the first of two articles, David Henwood discusses the vibrations that can be harnessed by musical instrument makers.
    [ PHYSICS ] 


3. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


4. Bigger bandwidth
   Plus Online Maths Magazine: News Story
    [ INFORMATION THEORY ] 


5. Stellar heartbeats
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


6. Career interview: Audio software engineer
   Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
    [ FOURIER ANALYSIS ] 


7. The magical mathematics of music
   According to Shakespeare, music is the food of love. But Jeffrey Rosenthal follows Galileo's observation that the entire universe is written in the language of mathematics - and that includes music.
    [ MATHEMATICS AND THE ARTS ] 


8. And the Oscar goes to...
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ]   [ MATHEMATICS AND THE ARTS ] 

FREQUENCY ANALYSIS

1. Cracking codes
   In the first of two articles, Artur Ekert takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 

FRICTION

1. Old problem, new spin
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


2. Hardboiled detectives
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

FUNDAMENTAL THEOREM OF ARITHMETIC

1. A whirlpool of numbers
   The Riemann Hypothesis is probably the hardest unsolved problem in all of mathematics, and one of the most important. It has to do with prime numbers - the building blocks of arithmetic. Nick Mee, together with Sir Arthur C. Clarke, tells us about the patterns hiding inside numbers.
    [ NUMBER THEORY ] 

FUND MANAGEMENT

1. Career interview: Actuarial researcher
   Shane Whelan likes a challenge, and his career path has been defined both by what he enjoyed and by a desire to keep learning. Becoming an actuary seemed like the perfect solution.
    [ ACTUARIAL SCIENCE ] 

FUTURE

1. Career interview: Financial modelling
   David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
    [ FINANCIAL MATHEMATICS ] 

FUTURE VALUE

1. Have we caught your interest?
   Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
    [ FINANCIAL MATHEMATICS ] 

FUZZY LOGIC

1. Fuzzy pizza
   Plus Online Maths Magazine: News Story
    [ ENGINEERING ] 

Back to the top

G

GöDEL'S INCOMPLETENESS THEOREM

1. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 


2. Omega and why maths has no TOEs
   Kurt Gödel, who would have celebrated his 100th birthday next year, showed in 1931 that the power of maths to explain the world is limited: his famous incompleteness theorem proves mathematically that maths cannot prove everything. Gregory Chaitin explains why he thinks that Gödel's incompleteness theorem is only the tip of the iceberg, and why mathematics is far too complex ever to be described by a single theory.
    [ PROOF ] 


3. Gödel and the limits of logic
   When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life.
    [ LOGIC ] 

GALILEO

1. Finding order in chaos
   All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
    [ CHAOS THEORY ] 

GAMBLING

1. Outer space: Racing certainties
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 


2. Let 'em roll
   Plus Online Maths Magazine: Feature Article
    [ PROBABILITY ] 

GAME DESIGN

1. Career interview: Games developer
   Andrew Wensley works at Eidos Interactive, the company who publish the mega-successful computer game Tomb Raider, featuring 90s icon Lara Croft. Andrew is a long-term computer game fan with an academic background in maths. PASS Maths caught up with him at Eidos's Wimbledon offices.
    [ COMPUTER SCIENCE ] 

GAME OF CHANCE

1. Mathematical mysteries: Getting the most out of life - Part 1
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

GAME OF LIFE

1. Looking at life with Gerardus 't Hooft
   Nobel Prizewinning Physicist Professor Gerardus 't Hooft has always been fascinated by the mathematical mysteries of nature. He tells Plus about his early life, and what our Universe might really be like.
    [ THEORETICAL PHYSICS ] 


2. Games, Life and the Game of Life
   When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
    [ GAME THEORY ] 

GAME OF NO CHANCE

1. What mathematicians get up to
   After 5,000 years, the game of Nine Men's Morris has succumbed to the power of modern computing, plus other recent mathematical discoveries in the world of games.
    [ GAME THEORY ] 

GAME THEORY

1. Adam Smith and the invisible hand
   Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
    [ FINANCIAL MATHEMATICS ] 


2. Playing the laying a pale egg game
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


3. Mathematical mysteries: What colour is my hat?
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 


4. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 


5. Love's a gamble
   Plus Online Maths Magazine: News Story
    [ GAME THEORY ] 


6. Game theory wins Nobel prize
   Plus Online Maths Magazine: News Story
    [ GAME THEORY ] 

GARRY KASPAROV

1. Practice makes perfect
   In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
    [ ARTIFICIAL INTELLIGENCE ] 

GAUSSIAN BLUR

1. Let there be light... (but not too much!)
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

GEAR

1. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 

GENERAL INSURANCE

1. Career Interview: Actuary
   Actuaries use mathematics to model the real world, finding business solutions to the perennial problems thrown up by life's uncertainties. Kathy Byrne tells Plus about life as Actuarial Director of an Insurance Company.
    [ FINANCIAL MATHEMATICS ] 

GENERAL RELATIVITY

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


2. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


3. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


4. Faster than a falling bullet...
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


5. Spinning in space
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

GENES

1. Career interview: Biomechanical engineer
   Jose Munoz explains how engineering can allow you to explore the unknown, from understanding how mechanical structures bend to investigating the way genes affect the shape of embryos.
    [ ENGINEERING ] 


2. Gene-ius
   Plus Online Maths Magazine: News Story
    [ GENES ] 

GENETICS

1. Nobel mathematics
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Understanding the noise
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

GENUS

1. Woman joins Adams family
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

GEODESIC

1. Time and motion
   Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.
    [ GEOMETRY ] 


2. The art of numbers
   At the Hewlett Packard campus in Bristol, a group of keen researchers are bringing together the worlds of advanced mathematics and fine art. Kona Macphee investigates.
    [ MATHEMATICS AND THE ARTS ] 


3. Imaging maths - Inside the Klein bottle
   In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.
    [ GEOMETRY ] 

GEODESIC DOME

1. The art of numbers
   At the Hewlett Packard campus in Bristol, a group of keen researchers are bringing together the worlds of advanced mathematics and fine art. Kona Macphee investigates.
    [ MATHEMATICS AND THE ARTS ] 


2. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

GEOMAGNETISM

1. Core business
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

GEOMETRIC ABSTRACTION

1. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

GEOMETRIC PATTERNS

1. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

GEOMETRIC SERIES

1. Have we caught your interest?
   Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
    [ FINANCIAL MATHEMATICS ] 


2. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ] 


3. Mathematical mysteries: Zeno's Paradoxes
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 


4. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 

GEOMETRISATION CONJECTURE

1. Mathematical millionaire?
   Plus Online Maths Magazine: News Story
    [ TOPOLOGY ] 

GEOMETRY

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Mathematical mysteries: The Solitaire Advance
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 


3. A Fields of their own
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS AND THE ARTS ] 


5. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 


6. Symmetry rules
   Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how not only shapes, but also laws of nature can be symmetrical, and how this aids our understanding of the universe.
    [ SYMMETRY ] 


7. Drinking coffee in the Klein Café
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 


8. Perfect buildings: the maths of modern architecture
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


9. Maths goes to the movies
   Plus Online Maths Magazine: Feature Article
    [ GEOMETRY ] 


10. "Read Euler, read Euler, he is the master of us all."
    Plus Online Maths Magazine: Feature Article
     [ HISTORY OF MATHEMATICS ] 


11. The Nature of Space and Time: An Evening of Speculation
    Plus Online Maths Magazine: News Story
     [ PHYSICS ] 


12. Troubled minds and perfect turbulence
    Plus Online Maths Magazine: News Story
     [ WEATHER ] 

GIFTEDNESS

1. Natural born mathematicians
   Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
    [ MATHEMATICAL THINKING ] 

GIMPS

1. Discovering new primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


2. Primes update: success again!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


3. Perilous primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


4. Of prime importance
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


5. Charity begins @home
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


6. New largest prime discovered!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


7. Volunteers discover new largest prime
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


8. Volunteers find largest prime number yet — again!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

GLOBAL POSITIONING SYSTEM

1. Lightning fast forecasts
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

GO

1. Games, Life and the Game of Life
   When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
    [ GAME THEORY ] 

GOLDBACH'S CONJECTURE

1. Mathematical mysteries: the Goldbach conjecture
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 


2. Mathematical mysteries: Goldbach revisited
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 


3. Gold for Goldbach
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

GOLDBACH CALCULATOR

1. Mathematical mysteries: Goldbach revisited
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

GOLDEN RATIO

1. The life and numbers of Fibonacci
   Fibonacci, famous for the Fibonacci sequence, also introduced the decimal system into Europe.
    [ NUMBER THEORY ] 


2. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 


3. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. The golden ratio and aesthetics
   It was Euclid who first defined the Golden Ratio, and ever since people have been fascinated by its extraordinary properties. Find out if beauty is in the eye of the beholder, and how the Golden Ratio crosses from mathematics to the arts.
    [ MATHEMATICS AND THE ARTS ] 


5. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

GOOGOL

1. Mathematics, marriage and finding somewhere to eat
   How do you choose a partner? Is it an irrational choice or is it made rationally, based on a mathematical model which analyses the best potential partner you are likely to meet?
    [ PROBABILITY ] 

GRAND UNIFIED THEORY

1. Roger Penrose: A Knight on the tiles
   Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
    [ THEORETICAL PHYSICS ] 


2. Looking at life with Gerardus 't Hooft
   Nobel Prizewinning Physicist Professor Gerardus 't Hooft has always been fascinated by the mathematical mysteries of nature. He tells Plus about his early life, and what our Universe might really be like.
    [ THEORETICAL PHYSICS ] 


3. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


4. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 

GRANULAR FLOW

1. Career interview: Avalanche researcher
   Jim McElwaine tells Plus how he combines his two loves - mathematics and mountaineering - in avalanche research.
    [ FLUID MECHANICS ] 


2. Going with the flow
   Fluid mechanics is the study of flows in both liquids and gases, and is therefore enormously important in understanding many natural phenomena, as well as in industrial applications. Geophysicist Herbert Huppert tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.
    [ FLUID MECHANICS ] 

GRAPH

1. Outer space: Is this a record?
   Plus Online Maths Magazine: Regular Item
    [ RECORD ] 


2. Graphical methods I: Slug wars
   To arm or to disarm? This is the question in Phil Wilson's article, which explores the maths behind a cold war in slug world.
    [ GRAPHICAL METHODS ] 


3. Graphical Methods II: The return of the slime
   In last issue's Graphical methods I Phil Wilson used maths to predict the outcome of a cold war in slug world. In this self-contained article he looks at slug world after the disaster: with only a few survivors and all infra-structure destroyed, which species will take root and how will they develop? Graphs can tell it all.
    [ GRAPHICAL METHODS ] 


4. Machine prose
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

GRAPHICAL METHODS

1. Graphical methods I: Slug wars
   To arm or to disarm? This is the question in Phil Wilson's article, which explores the maths behind a cold war in slug world.
    [ GRAPHICAL METHODS ] 


2. Graphical Methods II: The return of the slime
   In last issue's Graphical methods I Phil Wilson used maths to predict the outcome of a cold war in slug world. In this self-contained article he looks at slug world after the disaster: with only a few survivors and all infra-structure destroyed, which species will take root and how will they develop? Graphs can tell it all.
    [ GRAPHICAL METHODS ] 


3. Graphical methods III: the slugs bounce back
   Plus Online Maths Magazine: Feature Article
    [ GRAPHICAL METHODS ] 

GRAPH THEORY

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


2. Friends and strangers
   Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.
    [ COMBINATORICS ] 


3. Machine prose
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

GRAVITATIONAL LENSING

1. Faster than a falling bullet...
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

GRAVITATIONAL REDSHIFT

1. X-otic X-ray visions
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

GRAVITATIONAL WAVE DETECTOR

1. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 

GRAVITATIONAL WAVES

1. Faster than a falling bullet...
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

GRAVITY

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Planets, planets everywhere
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


3. Lensing helps see in the dark
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


4. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


5. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 


6. Happy Birthday Stephen Hawking!
   This issue of Plus is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his THEORETICAL PHYSICS ] 


7. Happy Birthday Stephen Hawking!
   Plus Online Maths Magazine: News Story
    [ THEORETICAL PHYSICS ] 


8. Faster than a falling bullet...
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


9. Outer space: Two's company, three's a crowd
   Plus Online Maths Magazine: Regular Item
    [ MECHANICS ] 


10. Lagrange and the Interplanetary Superhighway
    In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
     [ ASTRONOMY ] 


11. Outer space: A matter of gravity
    Plus Online Maths Magazine: Regular Item
     [ PHYSICS ] 


12. Fashion gets physical
    Plus Online Maths Magazine: News Story
     [ PHYSICS ] 


13. Brave young worlds
    Plus Online Maths Magazine: News Story
     [ ASTRONOMY ] 

GRAVITY CURRENT

1. Going with the flow
   Fluid mechanics is the study of flows in both liquids and gases, and is therefore enormously important in understanding many natural phenomena, as well as in industrial applications. Geophysicist Herbert Huppert tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.
    [ FLUID MECHANICS ] 

GREAT CIRCLE

1. Time and motion
   Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.
    [ GEOMETRY ] 

GROUP THEORY

1. The search for Higgs
   Plus Online Maths Magazine: News Story
    [ PARTICLE PHYSICS ] 


2. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


3. Genius, stupidity and genius again
   Tope Omitola looks back at the tragically short but inspiringly productive life of a true original: Evariste Galois.
    [ HISTORY OF MATHEMATICS ] 


4. The power of groups
   Groups are some of the most fundamental objects in maths. Take a system of interacting objects and strip it to the bone to see what makes it tick, and very often you're faced with a group. Colva Roney-Dougal takes us into their abstract world and puzzles over a game of Solitaire.
    [ GROUP THEORY ] 


5. An enormous theorem: the classification of finite simple groups
   Plus Online Maths Magazine: Feature Article
    [ GROUP THEORY ] 

GROUP VELOCITY

1. Faster than light
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


2. Light bends the 'wrong' way
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

GYROSCOPE

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 


2. Galloping gyroscopes
   If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.
    [ PHYSICS ] 


3. Hardboiled detectives
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

Back to the top

H

HAILSTONE EVALUATOR

1. Mathematical mysteries: Hailstone sequences
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

HAILSTONE SEQUENCE

1. Mathematical mysteries: Hailstone sequences
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 


2. More hailstones...
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

HALTING PROBLEM

1. What computers can't do
   Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
    [ COMPUTER SCIENCE ] 


2. Mathematical mysteries: Goldbach revisited
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

HAMILTON

1. Curious quaternions
   Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the first of two articles, he talks about connections between algebra and geometry, and the importance of lateral thinking in mathematics.
    [ ARITHMETIC ] 


2. Ubiquitous octonions
   Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.
    [ ARITHMETIC ] 

HAMMING CODE

1. Mathematical mysteries: What colour is my hat?
   Plus Online Maths Magazine: Regular Item
    [ COMBINATORICS ] 

HANDEDNESS

1. Through the looking-glass
   Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.
    [ GROUP THEORY ] 

HARDY

1. Remembrance of numbers past
   Memory is fundamental to the way we think, and we use it in almost every activity. But most of us cannot imagine approaching the level of world record holder Hiroyuki Goto, who memorised and recited 42,195 digits of pi! Rob Eastaway asks if mere mortals can learn anything useful from such incredible feats of memory, and gives some hints on how to remember numbers.
    [ MEMORY ] 

HARMONICS

1. Quake-proof
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

HARMONIC SERIES

1. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ] 


2. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 


3. Career interview: Audio software engineer
   Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
    [ FOURIER ANALYSIS ] 


4. Outer space: Is this a record?
   Plus Online Maths Magazine: Regular Item
    [ RECORD ] 


5. "Read Euler, read Euler, he is the master of us all."
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

HARMONIC WAVE

1. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 


2. Why is the violin so hard to play?
   As anyone starting out knows, the violin is a difficult instrument. It takes time before the novice player can expect to produce a musical note at the desired pitch, instead of a whistle, screech or graunch. Jim Woodhouse and Paul Galluzzo explain why.
    [ PHYSICS ] 

HARMONY

1. The magical mathematics of music
   According to Shakespeare, music is the food of love. But Jeffrey Rosenthal follows Galileo's observation that the entire universe is written in the language of mathematics - and that includes music.
    [ MATHEMATICS AND THE ARTS ] 

HASH ALGORITHM

1. The dangers of cracking hash
   Plus Online Maths Magazine: News Story
    [ CRYPTOGRAPHY ] 

HEAT DIFFUSION EQUATION

1. Career interview: Project finance consultant
   Nick Crawley had recently set up his own financial consultancy firm in Sydney, Australia, offering advice on large-scale financing deals. He tells Plus about the challenges and rewards of working in an incentive-driven environment.
    [ FINANCIAL MATHEMATICS ] 

HEDGING

1. Rogue trading?
   The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
    [ FINANCIAL MATHEMATICS ] 

HELICOIDAL SURFACE

1. Imaging maths - Inside the Klein bottle
   In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.
    [ GEOMETRY ] 

HELIOSEISMOLOGY

1. Career profile - Academic Researcher
   Find out how an early interest in Mathematics and Physics led Dr Helen Mason to a career in solar studies.
    [ PHYSICS ] 


2. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 


3. Stellar heartbeats
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

HELIX

1. Clever coiling
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

HELMHOLTZ VIBRATION

1. Why is the violin so hard to play?
   As anyone starting out knows, the violin is a difficult instrument. It takes time before the novice player can expect to produce a musical note at the desired pitch, instead of a whistle, screech or graunch. Jim Woodhouse and Paul Galluzzo explain why.
    [ PHYSICS ] 

HENRY PERIGAL

1. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 

HIGGS

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

HIGGS BOSON

1. The search for Higgs
   Plus Online Maths Magazine: News Story
    [ PARTICLE PHYSICS ] 

HIGGS FIELD

1. The search for Higgs
   Plus Online Maths Magazine: News Story
    [ PARTICLE PHYSICS ] 

HILBERT PROBLEMS

1. How maths can make you rich and famous: Part II
   One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
    [ HISTORY OF MATHEMATICS ] 


2. We must know, we will know
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 


3. Struggling for sixteen
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN THE MEDIA ] 

HILBERT SPACE-FILLING CURVE

1. The origins of fractals
   The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.
    [ GEOMETRY ] 

HISTORY OF MATHEMATICS

1. Daniel Bernoulli and the making of the fluid equation
   Daniel Bernoulli (1700-1782) discovered the relationship between the density of a fluid in a pipe, the speed it is travelling in the pipe and the pressure exerted by the fluid against the walls of the pipe. This is the story of what happened.
    [ FLUID MECHANICS ] 


2. The life and numbers of Fibonacci
   Fibonacci, famous for the Fibonacci sequence, also introduced the decimal system into Europe.
    [ NUMBER THEORY ] 


3. Mathematical mysteries: Kepler's conjecture
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


4. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


5. Prehistoric printer
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


6. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 


7. Dirac Centennial
   Plus Online Maths Magazine: News Story
    [ QUANTUM MECHANICS ] 


8. Newton and the kissing problem
   In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
    [ GEOMETRY ] 


9. Gödel and the limits of logic
   When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life.
    [ LOGIC ] 


10. The death of the lightning calculator
    Plus Online Maths Magazine: Feature Article
     [ ARITHMETIC ] 


11. We must know, we will know
    Plus Online Maths Magazine: Feature Article
     [ HISTORY OF MATHEMATICS ] 


12. "Read Euler, read Euler, he is the master of us all."
    Plus Online Maths Magazine: Feature Article
     [ HISTORY OF MATHEMATICS ] 


13. Outer space: Tally ho!
    Plus Online Maths Magazine: Regular Item
     [ HISTORY OF MATHEMATICS ] 

HOOKE'S LAW

1. Model behaviour
   To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
    [ MATHEMATICAL MODELLING ] 

HORSE RACING

1. Outer space: Racing certainties
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

HUBBLE TELESCOPE

1. Career interview: Science communicator
   Science writer and exhibition researcher Alison Boyle tells Plus about her work creating up-to-the-minute news exhibits at the Science Museum in London.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

HUFFMAN CODING

1. Text, Bytes and Videotape
   How can a 3 hour long film like the Lord of the Rings fit on a single DVD? Hw cn U rd txt msgs? How do MP3s make music files smaller, so they can be downloaded faster off the Internet? All these things rely on the mathematics of data compression.
    [ INFORMATION THEORY ] 

HUMAN CALCULATOR

1. Natural born mathematicians
   Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
    [ MATHEMATICAL THINKING ] 

HUMAN CONSCIOUSNESS

1. Roger Penrose: A Knight on the tiles
   Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
    [ THEORETICAL PHYSICS ] 

HYDROSTATICS

1. Probing the pint
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

HYPERBOLIC GEOMETRY

1. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


2. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


3. Bridges: mathematical connections in art and music
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 


4. Still life
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

HYPERCONE

1. The art of numbers
   At the Hewlett Packard campus in Bristol, a group of keen researchers are bringing together the worlds of advanced mathematics and fine art. Kona Macphee investigates.
    [ MATHEMATICS AND THE ARTS ] 

HYPOTHESIS TESTING

1. GM trials come a cropper
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

Back to the top

I

IDEAL

1. Against the odds
   Danielle Stretch looks back at the remarkable life of pioneering mathematician Emmy Amalie Noether (1882-1935). Despite her constant struggles to make her way in a man's world, she made significant contributions to the development of modern algebra.
    [ HISTORY OF MATHEMATICS ] 

IDENTITY

1. Through the looking-glass
   Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.
    [ GROUP THEORY ] 

IMAGE ANALYSIS

1. Image analysis - a modern application of mathematics
   New technology has provided us with some amazing images - satellite images, medical images, even images beamed back from Mars. Julian Stander tells us about the increasing role of statistics in interpreting them.
    [ STATISTICS ] 


2. Ancient maths recovered
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


3. Let there be light... (but not too much!)
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

IMAGE OF MATHS

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

INCOMPLETENESS THEOREM

1. We must know, we will know
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

INDEPENDENCE

1. Backgammon, doubling the stakes, and Brownian motion
   Backgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
    [ PROBABILITY ] 


2. Outer space: Independence Day
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 


3. Outer space: Rugby and Relativity
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

INDUCTION

1. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 

INDUSTRIAL MATHEMATICS

1. Career interview: Fluid mechanics researcher
   André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.
    [ FLUID MECHANICS ] 


2. Helping business make a crust
   Plus Online Maths Magazine: News Story
    [ INDUSTRIAL MATHEMATICS ] 

INERTIAL FRAME

1. What's so special about special relativity?
   Most of us are aware that Einstein proved that everything was relative ... or something like that. But we go no further, believing that we aren't clever enough to understand what he did. Hardeep Aiden sets out to persuade readers that they too can understand an idea as elegantly simple as it was original.
    [ SPECIAL RELATIVITY, ] 

INFINITE SERIES

1. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 


2. "Read Euler, read Euler, he is the master of us all."
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

INFINITY

1. A postcard from Italy
   Eugen Jost is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.
    [ MATHEMATICS AND THE ARTS ] 

INFLATION

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 

INFORMATION

1. Life as we don't know it
   Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
    [ ASTROBIOLOGY ] 

INFORMATION THEORY

1. Agner Krarup Erlang (1878 - 1929)
   The mathematics underlying today's complex telephone networks is still based on his work. Erlang was the first person to study the problem of telephone networks.
    [ HISTORY OF MATHEMATICS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

INKA

1. Not just knots: the secrets of khipu
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

INNATE MATHEMATICAL ABILITY

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

INSURANCE

1. Career interview - Actuarial Student
   Find out about what it is like to work as an actuary with Watson Wyatt Partners Worldwide. There's also salary information and a careers contact point.
    [ FINANCIAL MATHEMATICS ] 


2. Mathematical mysteries:
   Plus Online Maths Magazine: Regular Item
    [ HISTORY OF MATHEMATICS ] 


3. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 


4. Career interview: Actuarial researcher
   Shane Whelan likes a challenge, and his career path has been defined both by what he enjoyed and by a desire to keep learning. Becoming an actuary seemed like the perfect solution.
    [ ACTUARIAL SCIENCE ] 

INTEGRAL TEST

1. An infinite series of surprises
   Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
    [ ARITHMETIC ] 

INTERFERENCE

1. Radio controlled?
   We take reliable radio communications for granted, but accommodating many different users is not easy. Robert Leese explains how the mathematics of colouring graphs can help avoid interference on your mobile phone.
    [ PHYSICS ] 


2. Faster than light
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


3. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 

INTERNET SECURITY

1. The dangers of cracking hash
   Plus Online Maths Magazine: News Story
    [ CRYPTOGRAPHY ] 

INTERPLANETARY SUPERHIGHWAY

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

INTUITION

1. Maths on the brain
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL THINKING ] 

INVARIANT POINT

1. Fishy business
   'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
    [ BIOMATHEMATICS ] 

INVERSE PROBLEM

1. Crime fighting maths
   Maths is not the first thing that springs to mind when you think about fighting crime. But a closer look reveals that it is behind many of the techniques that modern detectives rely on. Chris Budd investigates.
    [ MATHEMATICS AND CRIME ] 

INVERSE SQUARE LAW

1. Mouthwatering maths
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

INVERSION

1. Through the looking-glass
   Some molecules - thalidomide, for example - come in both left and right handed versions, while others are indistinguishable from their reflections. Plus finds out about the role of mathematical symmetry in chemistry.
    [ GROUP THEORY ] 

INVISIBLE HAND

1. Adam Smith and the invisible hand
   Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
    [ FINANCIAL MATHEMATICS ] 

IRRATIONAL NUMBER

1. The origins of proof III: Proof and puzzles through the ages
   For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
    [ LOGIC ] 


2. Mathematical mysteries: Transcendental meditation
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

IRRATIONAL NUMBERS

1. Outer space: Some benefits of irrationality
   Plus Online Maths Magazine: Regular Item
    [ NUMBER THEORY ] 

ISAAC NEWTON

1. Newton and the kissing problem
   In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
    [ GEOMETRY ] 

ISBN

1. Take a break
   There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.
    [ CODES ] 

IT

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 

ITERATED PRISONERS' DILEMMA

1. Mathematical mysteries: Survival of the nicest?
   Plus Online Maths Magazine: Regular Item
    [ GAME THEORY ] 

ITERATION

1. Modelling nature with fractals
   Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
    [ GEOMETRY ] 


2. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 

Back to the top

J

JAVA APPLET

1. Using Java to enhance the WWW
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 

JULIA SET

1. Unveiling the Mandelbrot set
   Plus Online Maths Magazine: Feature Article
    [ FRACTAL ] 


2. Vaccination works
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 


3. A fat chance of chaos?
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 

Back to the top

K

KAPREKAR'S OPERATION

1. Mysterious number 6174
   6174 is a very mysterious number. Yutaka Nishiyama explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.
    [ NUMBER THEORY ] 

KEPLER

1. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 


2. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

KEPLER'S CONJECTURE

1. Mathematical mysteries: Kepler's conjecture
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN THE MEDIA ] 


3. Welcome to the maths lab
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

KEPLER'S THREE LAWS OF PLANETARY MOTION

1. The origins of proof II : Kepler's proofs
   Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.
    [ LOGIC ] 


2. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 

KERNEL

1. Mysterious number 6174
   6174 is a very mysterious number. Yutaka Nishiyama explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.
    [ NUMBER THEORY ] 

KEY DISTRIBUTION PROBLEM

1. Safety in numbers
   Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
    [ ENCRYPTION ] 

KHINCHIN'S CONSTANT

1. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 

KHIPU

1. Not just knots: the secrets of khipu
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

KINETIC ENERGY

1. Modelling, step by step
   Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.
    [ BIOMATHEMATICS ] 


2. Hardboiled detectives
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


3. In skimming, spin's the thing
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

KISSING PROBLEM

1. Newton and the kissing problem
   In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.
    [ GEOMETRY ] 

KLEIN BOTTLE

1. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS AND THE ARTS ] 


3. Imaging maths - Inside the Klein bottle
   In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.
    [ GEOMETRY ] 


4. Still life
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

KNOT

1. A knotty sartorial question
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 


2. Why knot: knots, molecules and stick numbers
   Knots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?
    [ TOPOLOGY ] 


3. Looking at life with Gerardus 't Hooft
   Nobel Prizewinning Physicist Professor Gerardus 't Hooft has always been fascinated by the mathematical mysteries of nature. He tells Plus about his early life, and what our Universe might really be like.
    [ THEORETICAL PHYSICS ] 

KNOTS IN CHEMISTRY

1. Why knot: knots, molecules and stick numbers
   Knots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?
    [ TOPOLOGY ] 

KNOT THEORY

1. Clever coiling
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

KOLMOGOROV'S AXIOMS OF PROBABILITY THEORY

1. What a coincidence!
   Coincidences are familiar to us all but what are the so-called laws of chance? From coin tossing to freak weather events, Geoffrey Grimmett explains how probability is at the heart of it all.
    [ PROBABILITY ] 

Back to the top

L

LABYRINTH

1. Maths aMazes
   

   C. J. Budd and C. J. Sangwin show us how to create mazes, and explain why mazes and networks have much in common. In fact the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion and conquest...
    [ TOPOLOGY ] 

LAGRANGE

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

LAGRANGE POINT

1. Mathematical mysteries: the three body problem
   Plus Online Maths Magazine: Regular Item
    [ ASTRONOMY ] 


2. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 


3. How not to catch a sunbeam
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 

LAGRANGIAN SYSTEM

1. Heavenly choreography
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

LAMBERT LAW OF ABSORPTION

1. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 

LANGUAGE

1. Speechless maths
   Plus Online Maths Magazine: News Story
    [ MATHS AND LANGUAGE ] 


2. Machine prose
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


3. Not just knots: the secrets of khipu
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

LAPLACE

1. Finding order in chaos
   All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
    [ CHAOS THEORY ] 

LARGE HADRON COLLIDER

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

LASER INTERFEROMETRY

1. Catching waves with Kip Thorne
   What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
    [ PHYSICS ] 

LATIN SQUARE

1. Anything but square: from magic squares to Sudoku
   Get on a commuter train these days and you can virtually see people's brains crunching away at filling the numbers from 1 to 9 into a square grid. As the Sudoku craze shows no sign of slowing, Hardeep Aiden investigates its relatives and predecessors.
    [ COMBINATORICS ] 

LATITUDE

1. Time and motion
   Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.
    [ GEOMETRY ] 

LATTICE TILING

1. On the dissecting table
   Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
    [ GEOMETRY ] 

LAW

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 


2. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 

LEAST SQUARES

1. Testing Bernoulli: a simple experiment
   Here is an experiment that you can easily do yourself to test Bernoulli's equation. There are also 2 questions and answers.
    [ FLUID MECHANICS ] 

LEBESGUE INTEGRATION

1. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

LEIBNIZ

1. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

LENS

1. Lensing helps see in the dark
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


2. Light bends the 'wrong' way
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

LEVY'S CONSTANT

1. Chaos in Numberland: The secret life of continued fractions
   One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
    [ NUMBER THEORY ] 

LEVY FLIGHT

1. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 

LHC

1. Secrets of the Universe — where size really does matter
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

LIBRARY OF BABEL

1. Dashing along
   Currently, disabled computer users have a hard time inputting text, using laborious word-completion. Plus find out how this is changing, thanks to Dasher, a new open-source text-entry system based on arithmetic coding.
    [ INFORMATION THEORY ] 

LIFE INSURANCE

1. Career Interview: Actuary
   Actuaries use mathematics to model the real world, finding business solutions to the perennial problems thrown up by life's uncertainties. Kathy Byrne tells Plus about life as Actuarial Director of an Insurance Company.
    [ FINANCIAL MATHEMATICS ] 


2. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 

LIFT

1. Understanding turbulence
   Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
    [ FLUID MECHANICS ] 

LIGHT ATTENUATION

1. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 

LIGHTNING PREDICTION

1. Lightning fast forecasts
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

LIMIT

1. The life and numbers of Fibonacci
   Fibonacci, famous for the Fibonacci sequence, also introduced the decimal system into Europe.
    [ NUMBER THEORY ] 


2. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 


3. Mathematical mysteries: Zeno's Paradoxes
   Plus Online Maths Magazine: Regular Item
    [ LOGIC ] 

LINEAR ALGEBRA

1. Relating relativity
   Plus Online Maths Magazine: News Story
    [ MATHS AND LANGUAGE ] 

LINEAR PROGRAMMING

1. I'm not paying that!
   It's not that long ago that all you needed to run an airline was a few planes and some competent pilots. But now, with more of us zipping around the globe every year and the advent of no frills airlines, keeping an airline competetive has become a complicated business. Christine Currie explains how your airfare is calculated.
    [ OPERATIONS RESEARCH ] 

LINKED PENDULUMS

1. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

LITERARY ANALYSIS

1. Outer space: Independence Day
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 


2. Outer space: Rugby and Relativity
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

LOCAL REALISM

1. Cracking codes, part II
   In the second of two articles, Artur Ekert visits the strange subatomic world and investigates the possibility of unbreakable quantum cryptography.
    [ CRYPTOGRAPHY ] 

LOGARITHM

1. Looking out for number one
   You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. Jon Walthoe explains why Benford's Law says otherwise, and why tax inspectors are taking an interest.
    [ NUMBER THEORY ] 


2. Jackson's fractals
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


3. Have we caught your interest?
   Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
    [ FINANCIAL MATHEMATICS ] 


4. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 


5. In perfect harmony
   The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
    [ ARITHMETIC ] 

LOGARITHMIC DECAY

1. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 


2. Radioactive decay and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the second of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses radioactive decay.
    [ PHYSICS ] 

LOGIC

1. Games, Life and the Game of Life
   When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
    [ GAME THEORY ] 


2. A bright idea
   What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
    [ LOGIC ] 


3. Gödel and the limits of logic
   When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life.
    [ LOGIC ] 


4. We must know, we will know
   Plus Online Maths Magazine: Feature Article
    [ HISTORY OF MATHEMATICS ] 

LOGIC GATE

1. Games, Life and the Game of Life
   When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
    [ GAME THEORY ] 


2. A bright idea
   What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
    [ LOGIC ] 

LOGISTIC MAP

1. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 

LONGITUDE

1. Time and motion
   Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.
    [ GEOMETRY ] 


2. 12:00 PMT?
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

LORENZ

1. Finding order in chaos
   All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
    [ CHAOS THEORY ] 


2. Chaotic crochet
   Plus Online Maths Magazine: News Story
    [ CHAOS THEORY ] 

LORENZ ATTRACTOR

1. Chaos in the brain
   Saying that someone is a chaotic thinker might seems like an insult - but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.
    [ CHAOS THEORY ] 

LORENZ EQUATIONS

1. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Chaotic crochet
   Plus Online Maths Magazine: News Story
    [ CHAOS THEORY ] 

LYAPUNOV EXPONENT

1. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 

LYAPUNOV FRACTAL

1. The art of numbers
   At the Hewlett Packard campus in Bristol, a group of keen researchers are bringing together the worlds of advanced mathematics and fine art. Kona Macphee investigates.
    [ MATHEMATICS AND THE ARTS ] 

LYAPUNOV STABILITY ANALYSIS

1. Robots can't play tennis - yet
   Plus Online Maths Magazine: News Story
    [ CHAOS THEORY ] 

Back to the top

M

MöBIUS STRIP

1. In space, do all roads lead to home?
   Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
    [ TOPOLOGY ] 


2. Still life
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ARTS ] 

M-THEORY

1. Stephen Hawking's 60 years in a nutshell
   Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.
    [ THEORETICAL PHYSICS ] 


2. Tying it all up
   Theoretical physicists are searching for a 'Theory of Everything' to reconcile quantum mechanics and relativity - the two great physical theories of the twentieth century. String theory is a current hot favourite, and some of the world's most eminent physicists tell us why.
    [ PARTICLE PHYSICS ] 


3. Building Newton's nest
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

MACLAURIN SERIES

1. Have we caught your interest?
   Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
    [ FINANCIAL MATHEMATICS ] 

MAGIC SQUARE

1. Maths and magic
   Until you understand the basics of functions and algebra, the thought that a number can be predicted is a surprising one. And of course `magic' and `being surprised' are often the same thing. Rob Eastaway shows us how mathemagicians trade off the fact that you can usually predict precisely the outcome of doing something in mathematics, but only if you know the secret beforehand.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. New designs from Africa
   Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
    [ GEOMETRY ] 


3. Anything but square: from magic squares to Sudoku
   Get on a commuter train these days and you can virtually see people's brains crunching away at filling the numbers from 1 to 9 into a square grid. As the Sudoku craze shows no sign of slowing, Hardeep Aiden investigates its relatives and predecessors.
    [ COMBINATORICS ] 

MAGIC TRICK

1. Maths and magic
   Until you understand the basics of functions and algebra, the thought that a number can be predicted is a surprising one. And of course `magic' and `being surprised' are often the same thing. Rob Eastaway shows us how mathemagicians trade off the fact that you can usually predict precisely the outcome of doing something in mathematics, but only if you know the secret beforehand.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MAGNETIC FIELD

1. The dynamic sun
   On 11th August 1999 a total eclipse of the Sun will be visible from parts of the UK. It will provide a spectacular display, but why is the Sun so interesting? Helen Mason explains.
    [ PHYSICS ] 


2. Bigger bandwidth
   Plus Online Maths Magazine: News Story
    [ INFORMATION THEORY ] 


3. Untangling a magnetic mystery
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

MALARIA

1. Help defeat malaria in Africa
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

MALTHUS

1. Population ex-explosion?
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

MANAGEMENT

1. Career interview: Business analyst
   From Einstein to water power, Plus author Anita King explains where maths has got her.
    [ BUSINESS ANALYSIS ] 

MANDELBROT SET

1. Unveiling the Mandelbrot set
   Plus Online Maths Magazine: Feature Article
    [ FRACTAL ] 


2. Vaccination works
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 


3. A fat chance of chaos?
   Plus Online Maths Magazine: News Story
    [ DYNAMICAL SYSTEM ] 

MANDELBROT SURFACE

1. Modelling nature with fractals
   Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
    [ GEOMETRY ] 

MANIFOLD

1. Lagrange and the Interplanetary Superhighway
   In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
    [ ASTRONOMY ] 

MAPLE

1. Interview: Maths student
   In this issue we talk to maths student Emily Dixon about her university studies, and where maths might take her in the future.
    [ MATHEMATICS EDUCATION ] 


2. Career interview: IT project manager
   Bharat Dodia tells Plus how his love of maths has taken him from turbulent times to building better IT systems for Ford.
    [ MATHEMATICS EDUCATION ] 

MARKOV PROCESS

1. Formulaic football
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


2. Understanding the noise
   Plus Online Maths Magazine: News Story
    [ BIOMATHEMATICS ] 

MARS

1. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MATERIAL PROPERTIES

1. Fashion gets physical
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

MATHEMATICAL MODELLING

1. Designing loudspeakers
   In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.
    [ PHYSICS ] 


2. Image analysis - a modern application of mathematics
   New technology has provided us with some amazing images - satellite images, medical images, even images beamed back from Mars. Julian Stander tells us about the increasing role of statistics in interpreting them.
    [ STATISTICS ] 


3. Career interview: Financial modelling
   David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
    [ FINANCIAL MATHEMATICS ] 


4. Career interview: Sales forecasting
   Helen Thompson works for Sainsbury's Supermarkets as a Sales Forecasting Manager. The Plus team paid her a visit at Drury House on the banks of the Thames in London.
    [ STATISTICS ] 


5. Career interview: Avalanche researcher
   Jim McElwaine tells Plus how he combines his two loves - mathematics and mountaineering - in avalanche research.
    [ FLUID MECHANICS ] 


6. Worldly wobbles
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


7. Light attenuation and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
    [ PHYSICS ] 


8. Modelling, step by step
   Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.
    [ BIOMATHEMATICS ] 


9. Radioactive decay and exponential laws
   Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the second of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses radioactive decay.
    [ PHYSICS ] 


10. Can cancer be cured?
    Plus Online Maths Magazine: News Story
     [ STATISTICS ] 


11. Career interview: Defence analyst
    Helen is a defence analyst with the MoD, using her maths skills to help defend the nation. Plus finds out about her career path.
     [ OPERATIONS RESEARCH ] 


12. How maths can make you rich and famous: Part II
    One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.
     [ HISTORY OF MATHEMATICS ] 


13. The crystal ball
    If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
     [ FINANCIAL MATHEMATICS ] 


14. Model behaviour
    To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
     [ MATHEMATICAL MODELLING ] 


15. Open wide...
    Plus Online Maths Magazine: News Story
     [ COMPUTER SCIENCE ] 


16. Career interview: Fluid mechanics researcher
    André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.
     [ FLUID MECHANICS ] 


17. Career interview: Biomechanical engineer
    Jose Munoz explains how engineering can allow you to explore the unknown, from understanding how mechanical structures bend to investigating the way genes affect the shape of embryos.
     [ ENGINEERING ] 


18. Matrix: Simulating the world
    
    Plus Online Maths Magazine: Feature Article
     [ COMPUTER SCIENCE ] 


19. Count-abel even if not solve-abel
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


20. Understanding the noise
    Plus Online Maths Magazine: News Story
     [ BIOMATHEMATICS ] 


21. Bracing for the storm
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS AND THE ENVIRONMENT ] 


22. Maths for the broken-hearted
    Plus Online Maths Magazine: News Story
     [ BIOMATHEMATICS ] 


23. And now, the weather...
    Plus Online Maths Magazine: News Story
     [ FLUID MECHANICS ] 


24. When will they blow?
    Plus Online Maths Magazine: News Story
     [ MATHEMATICAL MODELLING ] 

MATHEMATICAL MODELS

1. Imaging maths - Inside the Klein bottle
   In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.
    [ GEOMETRY ] 


2. Matrix: Simulating the world
   
   Plus Online Maths Magazine: Feature Article
    [ COMPUTER SCIENCE ] 


3. How to measure a million
   Plus Online Maths Magazine: News Story
    [ ECONOMICS ] 

MATHEMATICAL THINKING

1. Ubiquitous octonions
   Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.
    [ ARITHMETIC ] 

MATHEMATICS AND ART

1. Extracting beauty from chaos
   Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
   
    [ GEOMETRY ] 


2. Jackson's fractals
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


3. Fractal expressionism
   In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
    [ GEOMETRY ] 


4. Putting it in perspective
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


5. Getting into the picture
   Imagine stepping inside your favourite painting, walking around the light-filled music room of Vermeer's "The Music Lesson" or exploring the chapel in the "Trinity" painted by Masaccio in the 15th century. Using the mathematics of perspective, researchers are now able to produce three-dimensional reconstructions of the scenes depicted in these works.
    [ MATHEMATICS AND THE ARTS ] 


6. Career interview: Primary teacher
   Whether you love maths or hate maths, your opinions on the subject were probably formed early. So primary teachers have a vital role to play in promoting mathematical skills. Plus meets primary teacher and maths coordinator Maureen Matthews.
    [ MATHEMATICS EDUCATION ] 


7. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


8. ART+MATH=X
   Carla Farsi is both an artist and a mathematician, who declared 2005 her Special Year for art and maths. Find out what she got up to, and what it's like being a part of both worlds.
    [ MATHEMATICS AND THE ARTS ] 


9. Career interview: furniture design
   Two designers tell us how they took the long way round to design, and how the maths and science they took in on the way helps them with their work today.
    [ MATHEMATICS AND THE ARTS ] 


10. Bridges: mathematical connections in art and music
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS AND THE ARTS ] 


11. Still life
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS AND THE ARTS ] 

MATHEMATICS AND COMPUTERS

1. Searching for the soul in the machine
   Plus Online Maths Magazine: News Story
    [ MATHS AND COMPUTERS ] 


2. Hide and seek
   Plus Online Maths Magazine: News Story
    [ MATHS AND COMPUTERS ] 

MATHEMATICS AND CRIME

1. Crime fighting maths
   Maths is not the first thing that springs to mind when you think about fighting crime. But a closer look reveals that it is behind many of the techniques that modern detectives rely on. Chris Budd investigates.
    [ MATHEMATICS AND CRIME ] 

MATHEMATICS AND LANGUAGE

1. Relating relativity
   Plus Online Maths Magazine: News Story
    [ MATHS AND LANGUAGE ] 

MATHEMATICS AND MAGIC

1. 1089 and all that
   Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
    [ PROOF ] 

MATHEMATICS AND MUSIC

1. Natural frequencies and music
   In the first of two articles, David Henwood discusses the vibrations that can be harnessed by musical instrument makers.
    [ PHYSICS ] 


2. Designing loudspeakers
   In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.
    [ PHYSICS ] 


3. Self-similar syncopations:
   Fibonacci, L-systems, limericks and ragtime
   Kevin Jones investigates the links between music and mathematics, throwing in limericks, Fibonacci and Scott Joplin along the way. Plus is proud to present an extended version of his winning entry for the THES/OUP 1999 Science Writing Prize.
    [ MATHEMATICS AND THE ARTS ] 


4. Music to their ears
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL THINKING ] 


5. Career interview: Audio software engineer
   Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
    [ FOURIER ANALYSIS ] 


6. Why is the violin so hard to play?
   As anyone starting out knows, the violin is a difficult instrument. It takes time before the novice player can expect to produce a musical note at the desired pitch, instead of a whistle, screech or graunch. Jim Woodhouse and Paul Galluzzo explain why.
    [ PHYSICS ] 


7. The magical mathematics of music
   According to Shakespeare, music is the food of love. But Jeffrey Rosenthal follows Galileo's observation that the entire universe is written in the language of mathematics - and that includes music.
    [ MATHEMATICS AND THE ARTS ] 


8. Career interview: computer music researcher
   Teaching a machine to understand music is an incredibly difficult task, which uses all the mathematical power of digital signal processing. But teaching a machine to compose music is quite another matter, and the wonderful world of mathematical patterns proves to be a gold mine. Nick Collins talks to Plus about his artifical musician.
    [ MATHEMATICS AND THE ARTS ] 


9. Music and Euclid's algorithm
   Plus Online Maths Magazine: Feature Article
    [ MATHEMATICS AND THE ARTS ] 


10. Lost in music
    Plus Online Maths Magazine: News Story
     [ NETWORK ] 


11. Bridges: mathematical connections in art and music
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS AND THE ARTS ] 

MATHEMATICSAND RELIGION

1. John D Barrow wins Templeton Prize
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

MATHEMATICS AND THE ENVIRONMENT

1. Bracing for the storm
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS AND THE ENVIRONMENT ] 


2. How plants halt sands
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

MATHEMATICS ANXIETY

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MATHEMATICS EDUCATION

1. Career profile - Academic Researcher
   Find out how an early interest in Mathematics and Physics led Dr Helen Mason to a career in solar studies.
    [ PHYSICS ] 


2. Career interview - Accountant
   We talk to Tim Pilkington, a keen basketball player, who has a joint honours BSc in Maths, Physical Education and Sports Science from Loughborough University. Tim has worked as a mathematics teacher and is now working as an accountant.
    [ FINANCIAL MATHEMATICS ] 


3. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. Career interview - Qualifications Manager
   Karen Reid, whose hobbies include badminton and salsa dancing, is a Maths graduate. She works as a Qualifications Manager at RSA Examinations Board, Coventry and has also taught Maths.
    [ MANAGEMENT ] 


6. Join NRICH - the online maths club
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


7. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


8. Maths adds up
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


9. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


10. Maths Year 2000
    Plus Online Maths Magazine: News Story
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


11. Opinion
    Plus Online Maths Magazine: Regular Item
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


12. Opinion
    Plus Online Maths Magazine: Regular Item
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


13. Career interview: Maths editor
    Plus talks to Jon Walthoe, a commissioning editor for maths book, about finding new books, windsurfing and choosing a career.
     [ MATHEMATICAL WRITING ] 


14. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ CAREERS IN MATHEMATICS ] 


15. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ MATHEMATICS EDUCATION ] 


16. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ MATHEMATICS EDUCATION ] 


17. Career interview: maths teacher
    Adrian Dow has a huge change ahead of him: after fourteen years in the UK and around the world, he's about to return to his native Trinidad with the ultimate aim to open his own school. Plus intercepted him on the way to the airport.
     [ MATHEMATICS EDUCATION ] 


18. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ PLUS NEW WRITERS AWARD ] 


19. How time does PASS
    Plus Online Maths Magazine: Feature Article
     [ MATHEMATICS IN THE MEDIA ] 


20. Post-14 post-Smith
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


21. Will new maths GCSEs leave students unprepared?
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 


22. Happy birthday, Plus!
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


23. Maths on the wall
    Plus Online Maths Magazine: News Story
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


24. Teaching excellence
    Plus Online Maths Magazine: News Story
     [ MATHS EDUCATION ] 


25. Convergence: Where Mathematics, History and Teaching Interact
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 


26. The Further Maths Network has been launched
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 


27. North and south
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 


28. Royal recognition
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 


29. Connections in space
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS EDUCATION ] 

MATHEMATICS ENRICHMENT

1. Join NRICH - the online maths club
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Career interview: Primary teacher
   Whether you love maths or hate maths, your opinions on the subject were probably formed early. So primary teachers have a vital role to play in promoting mathematical skills. Plus meets primary teacher and maths coordinator Maureen Matthews.
    [ MATHEMATICS EDUCATION ] 


3. Convergence: Where Mathematics, History and Teaching Interact
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 


4. The Further Maths Network has been launched
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 


5. North and south
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 

MATHEMATICS IN FILMS

1. Fields medals
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Maths in the movies
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MATHEMATICS IN SPORT

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS IN SPORT ] 


2. Outer space: Tally ho!
   Plus Online Maths Magazine: Regular Item
    [ HISTORY OF MATHEMATICS ] 


3. The luck of the draw
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


4. Eye on the ball
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS IN SPORT ] 

MATHEMATICS IN THE MEDIA

1. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 


2. Opinion
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICAL MODELLING ] 


3. More or Less
   A new series of More or Less, BBC Radio 4's series devoted to all things numerical, starts on November 12th. Presenter Andrew Dilnot tells Plus about the motivation behind the programme.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 


5. From kaleidoscopes to soccer balls
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 


6. GM trials come a cropper
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 


7. Mind the gap
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


8. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


9. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ MATHEMATICS EDUCATION ] 


10. Einstein as icon
    One hundred years ago, in 1905, Albert Einstein changed physics forever with his special theory of relativity. Since then his name — and hair do — have become synonymous with genius. John D Barrow looks at Einstein as a media star.
     [ MATHEMATICS IN THE MEDIA ] 


11. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ MATHEMATICS IN THE MEDIA ] 


12. Damn lies
    Plus Online Maths Magazine: Feature Article
     [ STATISTICS ] 


13. Pluschat
    Plus Online Maths Magazine: Regular Item
     [ MATHEMATICS IN THE MEDIA ] 


14. How time does PASS
    Plus Online Maths Magazine: Feature Article
     [ MATHEMATICS IN THE MEDIA ] 


15. Plus appears on Doctor Who!
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


16. Here goes the Sun
    Plus Online Maths Magazine: News Story
     [ NETWORK ] 


17. Innate geometry
    Plus Online Maths Magazine: News Story
     [ NETWORK ] 


18. Lost in music
    Plus Online Maths Magazine: News Story
     [ NETWORK ] 


19. John D Barrow wins Templeton Prize
    Plus Online Maths Magazine: News Story
     [ ASTRONOMY ] 


20. Happy birthday, Plus!
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


21. Maths on the wall
    Plus Online Maths Magazine: News Story
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


22. Seeking truth with statistics
    Plus Online Maths Magazine: News Story
     [ STATISTICS ] 


23. Burning buried sunshine
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


24. Struggling for sixteen
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


25. Near miss or normal?
    Plus Online Maths Magazine: News Story
     [ MATHEMATICS IN THE MEDIA ] 


26. Million dollar maths
    Plus Online Maths Magazine: News Story
     [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


27. Who do you trust?
    Plus Online Maths Magazine: News Story
     [ STATISTICS ] 


28. Rap: rivalry and chivalry
    Plus Online Maths Magazine: News Story
     [ NETWORK ] 


29. Body count
    Plus Online Maths Magazine: News Story
     [ STATISTICS ] 

MATHEMATICS OF GROWTH

1. Fishy business
   'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
    [ BIOMATHEMATICS ] 

MATHEMATICS VOCABULARY

1. Mathematically fluent
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 

MATHS YEAR 2000

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Maths Year 2000
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MATRIX

1. New designs from Africa
   Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
    [ GEOMETRY ] 


2. Getting into the picture
   Imagine stepping inside your favourite painting, walking around the light-filled music room of Vermeer's "The Music Lesson" or exploring the chapel in the "Trinity" painted by Masaccio in the 15th century. Using the mathematics of perspective, researchers are now able to produce three-dimensional reconstructions of the scenes depicted in these works.
    [ MATHEMATICS AND THE ARTS ] 

MAXIMISATION

1. Mathematical mysteries: Getting the most out of life - Part 1
   Plus Online Maths Magazine: Regular Item
    [ PROBABILITY ] 

MAXIMUM LIKELIHOOD

1. Cat count
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 

MAXWELL'S EQUATIONS OF ELECTROMAGNETISM

1. Light bends the 'wrong' way
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 


2. Core business
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

MAZE

1. Maths aMazes
   

   C. J. Budd and C. J. Sangwin show us how to create mazes, and explain why mazes and networks have much in common. In fact the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion and conquest...
    [ TOPOLOGY ] 

MAZE SEED

1. Maths aMazes
   

   C. J. Budd and C. J. Sangwin show us how to create mazes, and explain why mazes and networks have much in common. In fact the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion and conquest...
    [ TOPOLOGY ] 

MBUTTON

1. Mathematically fluent
   Plus Online Maths Magazine: News Story
    [ MATHEMATICS EDUCATION ] 

MEAN

1. All about averages
   Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.
    [ STATISTICS ] 


2. Damn lies
   Plus Online Maths Magazine: Feature Article
    [ STATISTICS ] 

MEASURABILITY

1. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

MEASURE THEORY

1. Measure for measure
   Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
    [ GEOMETRY ] 

MECHANICAL CALCULATOR

1. Why Was The Computer Invented When It Was?
   Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
    [ COMPUTER SCIENCE ] 

MECHANICS

1. Old problem, new spin
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

MEDIAN

1. All about averages
   Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.
    [ STATISTICS ] 


2. Damn lies
   Plus Online Maths Magazine: Feature Article
    [ STATISTICS ] 

MEDICAL STATISTICS

1. The best medicine?
   To make hard decisions, you need hard facts. Medical statistics can help us to decide what treatment to look for when we are ill, and to estimate our chances of recovery.
    [ STATISTICS ] 


2. Career interview: Medical statistician
   Ever since the thalidomide tragedy, governments have realised the importance of a strict licensing regime for new drugs. Medical statistician Robert Hemmings explains how his work for the Medicines Control Agency helps to safeguard the health of the nation.
    [ STATISTICS ] 


3. Can cancer be cured?
   Plus Online Maths Magazine: News Story
    [ STATISTICS ] 


4. Altimeters, accidents and air traffic controllers
   Geoff Wilson is an air traffic controller for the Royal Air Force. Recently back from Kabul in Afghanistan, he tells Plus how logical thinking under pressure is crucial in his job.
    [ STATISTICS ] 

MEDICINE

1. Nobel mathematics
   Plus Online Maths Magazine: News Story
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Understanding influenza
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 


3. O.R. shortens kidney queues
   Plus Online Maths Magazine: News Story
    [ OPERATIONS RESEARCH ] 


4. Help defeat malaria in Africa
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL MODELLING ] 

MENTAL ARITHMETIC

1. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


2. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


3. Pluschat
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


4. The death of the lightning calculator
   Plus Online Maths Magazine: Feature Article
    [ ARITHMETIC ] 

MERCATOR PROJECTION

1. Mathematical mysteries: Strange Geometries
   Plus Online Maths Magazine: Regular Item
    [ GEOMETRY ] 

MERIDIAN

1. 12:00 PMT?
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

MERSENNE PRIME

1. Discovering new primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


2. Primes update: success again!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


3. Perilous primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 


4. Of prime importance
   Plus Online Maths Magazine: News Story
    [ COMPUTER SCIENCE ] 


5. Volunteers discover new largest prime
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

MERSENNE PRIMES

1. New largest prime discovered!
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

MERSENNE SEARCH

1. Perilous primes
   Plus Online Maths Magazine: News Story
    [ NUMBER THEORY ] 

META-ANALYSIS

1. The best medicine?
   To make hard decisions, you need hard facts. Medical statistics can help us to decide what treatment to look for when we are ill, and to estimate our chances of recovery.
    [ STATISTICS ] 

METEORITE

1. All about asteroids
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

METEOROLOGY

1. Long range forecast
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


2. Career interview - Meteorologist
   Read about what it is like to work at the Meteorological Office in this interview with Helen Hewson. There's also a contact point for careers information.
    [ FLUID MECHANICS ] 


3. Doing the twist
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 


4. Maths on the tube
   During World Mathematical Year 2000, a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 


5. And now, the weather...
   Plus Online Maths Magazine: News Story
    [ FLUID MECHANICS ] 

MILLENNIUM

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MILLENNIUM BUG

1. Editorial
   Plus Online Maths Magazine: Regular Item
    [ PUBLIC UNDERSTANDING OF MATHEMATICS ] 

MINIMAL CRIMINAL

1. The origins of proof IV: The philosophy of proof
   Robert Hunt concludes our Origins of Proof series by asking what a proof really is, and how we know that we've actually found one. One for the philosophers to ponder...
    [ LOGIC ] 

MINIMAL ENERGY

1. Mouthwatering maths
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

MINIMAL SURFACE

1. Double bubble is no trouble
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 


2. Maths and art: the whistlestop tour
   Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.
    [ MATHEMATICS AND THE ARTS ] 

MIXED STRATEGY

1. Game theory and the Cuban missile crisis
   Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.
    [ GAME THEORY ] 

MODE

1. Natural frequencies and music
   In the first of two articles, David Henwood discusses the vibrations that can be harnessed by musical instrument makers.
    [ PHYSICS ] 

MODULAR ARITHMETIC

1. Take a break
   There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.
    [ CODES ] 

MOMENT OF INERTIA

1. Unspinning the boomerang
   In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
    [ AERODYNAMICS ] 


2. The right spin: how to fly a broken space craft
   On the 25th of May 1997 a dramatic collision tore a hole into the space station Mir and sent it hurtling through space. As NASA astronaut Michael Foale tells Plus, the fate of Mir and its crew hinged on a classical set of equations.
    [ ASTRONOMY ] 

MOMENTUM

1. Light's identity crisis
   What is light? Sometimes it seems wave-like and sometimes particle like. See how Einstein applied his theory of relativity to the problem, predicted that photons have no mass and laid the foundations for quantum mechanics.
    [ QUANTUM MECHANICS ] 

MONOPOLY BOARD GAME

1. Monte Carlo Monopoly
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 

MONTE CARLO METHOD

1. Monte Carlo Monopoly
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 


2. Reducing radiotherapy roulette
   Plus Online Maths Magazine: News Story
    [ PROBABILITY ] 

MORPHOGENESIS

1. How the leopard got its spots
   How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Lewis Dartnell solves these, and other, puzzles of animal patterning.
    [ DIFFERENTIAL EQUATIONS ] 

MORTALITY TABLE

1. Death and statistics
   Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
    [ FINANCIAL MATHEMATICS ] 

MOZART

1. Music to their ears
   Plus Online Maths Magazine: News Story
    [ MATHEMATICAL THINKING ] 

MULTILATERATION

1. Parallel parking
   Plus Online Maths Magazine: News Story
    [ GEOMETRY ] 

MULTISPECTRAL IMAGING

1. Ancient maths recovered
   Plus Online Maths Magazine: News Story
    [ HISTORY OF MATHEMATICS ] 

MULTISTATE MODELLING

1. The crystal ball
   If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
    [ FINANCIAL MATHEMATICS ] 

MUON

1. What's so special about special relativity?
   Most of us are aware that Einstein proved that everything was relative ... or something like that. But we go no further, believing that we aren't clever enough to understand what he did. Hardeep Aiden sets out to persuade readers that they too can understand an idea as elegantly simple as it was original.
    [ SPECIAL RELATIVITY, ] 

MUSIC INDUSTRY

1. Career interview: Film marketing analyst
   Francesca Harris has always known she wanted to work in the music or film industry, and she has found that her maths skills have stood her in good stead as she works her way up.
    [ MARKETING ] 

Back to the top

N

NASA

1. Martian mayhem
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 


2. Mission to Mars
   Plus Online Maths Magazine: News Story
    [ SPACE EXPLORATION ] 


3. Brave young worlds
   Plus Online Maths Magazine: News Story
    [ ASTRONOMY ] 

NASH EQUILIBRIUM

1. Game theory and the Cuban missile crisis
   Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.
    [ GAME THEORY ] 


2. Love's a gamble
   Plus Online Maths Magazine: News Story
    [ GAME THEORY ] 


3. Game theory wins Nobel prize
   Plus Online Maths Magazine: News Story
    [ GAME THEORY ] 

NATURAL FREQUENCY

1. Quake-proof
   Plus Online Maths Magazine: News Story
    [ PHYSICS ] 

NATURAL SELECTION

1. Life as we don't know it
   Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
    [ ASTROBIOLOGY ] 

NAUTILUS LOUDSPEAKER

1. Designing loudspeakers
   In his second article, David Henwood explains the role of mathematics in the design of Hi-Fi loudspeakers.
    [ PHYSICS ] 

NAVIER-STOKES EQUATIONS

1. Understanding turbulence
   Have you ever been in an aeroplane on a smooth flight when suddenly t