File:Klein_bottle.svg · Wikimedia Commons · See Wikimedia Commons
Klein bottle
Sign in to savetype of non-orientable surface
Wikidata facts
- Image
- Acme klein bottle.jpg
Show 3 more facts
- Commons category
- Klein bottle
- time of discovery or invention
- 1882-00-00
- Euler characteristic
- 0
via Wikidata · CC0
~16 min read
Article
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.
Gallery (12)
Connections
covering space
Entity
surface
Entity
torus
Entity
Möbius strip
Entity
manifold
Entity
vector bundle connection
Entity
mathematics
Entity
International Standard Book Number
Entity
circle
Entity
square
Entity
sphere
Entity
macOS
Entity
digital object identifier
Entity
cylinder
Entity
three-dimensional space
Entity
Felix Klein
Entity
continuous function
Entity
Cartesian product
Entity
disk
Entity
Euclidean space
Entity