Klein bottle

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.

Tags: cosmology : compact universe : connectedness : Möbius strip : Klein bottle : tiling : curvature

Some people think science is worthwhile because it is useful; some argue that it also increases our aesthetic appreciation of art and nature. But you rarely hear anyone argue that science is beautiful in itself. With the start of our new series "Imaging maths", Plus argues for recognition of a mathematical aesthetic.

Tags: Klein bottle : geometry : aesthetics

In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.

Tags: Klein bottle : mathematical modelling : topology : visualisation : projective plane : surface : orientability : one-sided surface : two-sided surface : torus : helicoidal surface : geodesic

Lucinda Mathews visualises tricky surfaces

Tags: Möbius strip : Klein bottle : permutation : hyperbolic geometry : topology

Mathematics illustrates the forefront of visualising science

Tags: Möbius strip : Klein bottle : mathematics and art : hyperbolic geometry : visualisation : elliptic geometry

Conversations across science and art

Tags: Klein bottle : mathematics and art : architecture : sculpture