In mathematics, the Klein bottle ( /ˈklaɪn/) is a non-orientable surface, informally, a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface 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 that this was incorrectly interpreted as Kleinsche Flasche ("Klein bottle"), which ultimately led to the adoption of this term in the German language as well.
Read more about Klein Bottle: Construction, Properties, Dissection, Simple-closed Curves, Parameterization, Generalizations, Klein Surface
Famous quotes containing the word bottle:
“Kelly: I washed my face clean the morning I woke up in your bedroom.
Griff: You got morals in my bedroom?
Kelly: You had nothing to do with it. Nothing! It was your mirror.
Griff: You must have taken a long look.
Kelly: It was the longest look of my life. I saw a broken-down piece of machinery. Nothing but the buck, the bed, and the bottle for the rest of my life.”
—Samuel Fuller (b. 1911)