File:Klein_bottle.svg · Wikimedia Commons · See Wikimedia Commons
Klein bottle
Sign in to savetype of non-orientable surface
Wikidata facts
- Named after
- Felix Klein
- Image
- Acme klein bottle.jpg
Show 6 more facts
- Commons category
- Klein bottle
- time of discovery or invention
- 1882-00-00
- discoverer or inventor
- Felix Klein
- Euler characteristic
- 0
- maintained by WikiProject
- WikiProject Mathematics
- different from
- impossible bottle
via Wikidata · CC0
~16 min read
Encyclopedic overview
A two-dimensional representation of the Klein bottle immersed in three-dimensional space
In mathematics, the Klein bottle (/ˈklaɪn/) is an example of a surface with no distinct inside or outside. In other words, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, it is an example of a non-orientable surface, a two-dimensional manifold on which one cannot define a consistent direction perpendicular to the surface (normal vector) that varies continuously over the whole shape.
Excerpted from Wikipedia’s “Klein bottle” article, available under the CC BY-SA 4.0 licence.