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:
“Let us not succumb to nature. We will marshall the clouds and restrain tempests; we will bottle up pestilent exhalations; we will probe for earthquakes, grub them up, and give vent to the dangerous gas; we will disembowel the volcano, and extract its poison, take its seed out. We will wash water, and warm fire, and cool ice, and underprop the earth. We will teach birds to fly, and fishes to swim, and ruminants to chew the cud. It is time we looked into these things.”
—Henry David Thoreau (1817–1862)