The Klein bottle is a non-orientable surface with no distinct inside or outside: a one-sided surface that, if traveled upon, returns to its starting point flipped as though reflected. Felix Klein first described it in 1882. It cannot be embedded in three-dimensional Euclidean space without self-intersecting, unlike the Mobius strip, though it embeds cleanly in four dimensions. The Klein bottle is homeomorphic to the connected sum of two real projective planes and, unlike the Mobius strip, is a closed surface with no boundary.
Facts
FAQs
What happens if you cut a Klein bottle in half?
Cut along its length it gives two Möbius strips.
Cut in half along its length, a Klein bottle makes two Möbius strips. It can also be cut into a single Möbius strip instead, so the result depends on how the cut is made.
Connections
Attributed To
Source Klein Bottle (Wikipedia)
In Branch
Source Klein Bottle (Wikipedia)
Is Kind Of Object
Principal Result Of
Source Klein Bottle (Wikipedia)
Sources
1. Klein Bottle (Wikipedia)
Wikimedia FoundationLead section
In mathematics, the Klein bottle () is an example of a surface with no distinct inside or outside.
Lead section, dimension
a non-orientable surface, a two-dimensional manifold
- In Branch: Topology
Principal Result Of: Felix Klein, Lead sentence of the article on the result
The Klein bottle was first described in 1882 by the mathematician Felix Klein.
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