Klein bottle

Noun

Meaning

a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end

Hypernyms

Examples

3D pinched torus / 4D Möbius tube The pinched torus immersion of the Klein bottle. Source: Internet

A Klein bottle can be produced by gluing two Möbius strips together along their edges; this cannot be done in ordinary three-dimensional Euclidean space without creating self-intersections. Source: Internet

For example, the Klein bottle is a surface, which cannot be represented in the three-dimensional Euclidean space without introducing self-intersections (it cannot be embedded in the three dimensional Euclidean space). Source: Internet

Immersed Klein bottles in the Science Museum in London A hand-blown Klein Bottle The common physical model of a Klein bottle is a similar construction. Source: Internet

Nonetheless, there is a way to visualize the Klein bottle as being contained in four dimensions. Source: Internet

Note that the sphere and the projective plane can both be realized as quotients of the 2-gon, while the torus and Klein bottle require a 4-gon (square). Source: Internet

Close letter words and terms