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:
“Well, you look so pretty in it
Honey, can I jump on it sometime?
Yes, I just wanna see
If it’s really that expensive kind
You know it balances on your head
Just like a mattress balances
On a bottle of wine
Your brand new leopard-skin pill-box hat.”
—Bob Dylan [Robert Allen Zimmerman] (b. 1941)