The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix Klein (Hilbert and Cohn-Vossen 1999, p. 308). It can be constructed by gluing both pairs of opposite edges of a rectangle together giving one pair a half-twist, but can be physically realized only in four dimensions, since it must pass through itself without the presence of a hole. Its topology is equivalent to a pair of cross-caps with coinciding boundaries (Francis and Weeks 1999). (Wolfram)
FAQs
Q: Can I put water in a Klein bottle?
A: Yes.
Q: Can I get the water out, once I pour it in?
A: Good luck.
Q: Of what use is a Klein bottle?
A: Of what use is a newborn baby?
Q: With a Klein bottle, can I travel in time?
A: Yes. Forward.