One-Sided Surface

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one-sided surface [′wən ‚sīd·əd ′sər·fəs]

(mathematics)

A surface such that an object resting on one side can be moved continuously over the surface to reach the other side without going around an edge; the Möbius band and the Klein bottle are examples. Also known as nonorientable surface.

One-Sided Surface

a surface that, in contrast to, for example, the sphere or square, does not have two different sides. More precisely, let us suppose the surface has a normal continuously dependent on a point. By taking the normal vector at any point on the surface and continuously shifting it along a closed path, we can reach the initial point with a vector opposite in direction to the original vector. The simplest one-sided surface is the Möbius band. The class of one-sided surfaces in three-dimensional space coincides with the class of nonorientable surfaces.

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