In mathematics, the Klein bottle is a certain non-orientable surface, i.e., a surface (a two-dimensional topological space) with no distinct “inner” and “outer” sides. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a two dimensional object with one side and one edge, a Klein bottle is a two dimensional object with one side and no edges. (For comparison, a sphere is a two dimensional object with no edges and two sides.)
The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It was originally named the Kleinsche Fläche “Klein surface”; however, this was incorrectly interpreted as Kleinsche Flasche “Klein bottle”, which ultimately led to the adoption of this term in the German language as well.