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:
“I fasted for some forty days on bread and buttermilk
For passing round the bottle with girls in rags or silk,
In country shawl or Paris cloak, had put my wits astray,
And what’s the good of women for all that they can say
Is fol de rol de rolly O.”
—William Butler Yeats (1865–1939)