Klein bottle [SEP] named after
with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).
The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It may have been originally named the "Kleinsche Fläche" ("Klein surface") and then misinterpreted as "Kleinsche Flasche" ("Klein bottle"), which ultimately may have led to the adoption of this term in the German language as well.
Construction.
The following square is a fundamental
was to have a major role in his later work. Klein also learned about groups from Camille Jordan.
Klein devised the "Klein bottle" named after him, a one-sided closed surface which cannot be embedded in three-dimensional Euclidean space, but it may be immersed as a cylinder looped back through itself to join with its other end from the "inside". It may be embedded in the Euclidean space of dimensions 4 and higher. The concept of a Klein Bottle was devised as a 3-Dimensional Möbius