Klein bottle

noun Geometry.

a one-sided figure consisting of a tapered tube the narrow end of which is bent back, run through the side of the tube, and flared to join the wide end, thereby allowing any two points on the figure to be joined by an unbroken line.

Origin of Klein bottle

First recorded in 1940–45; named after F. Klein

British Dictionary definitions for klein bottle

Klein bottle
/ (klaɪn) /

noun

maths a surface formed by inserting the smaller end of an open tapered tube through the surface of the tube and making this end contiguous with the other end

Word Origin for Klein bottle

named after Felix Klein (1849–1925) German mathematician

Scientific definitions for klein bottle

Klein bottle
[ klīn ]

A smooth surface that has no inside or outside. It is often pictured in ordinary space as a tube that bends back upon itself, entering through the side and joining with the open end. A true Klein bottle, which cannot be constructed in ordinary three-dimensional space, would not actually intersect itself. The Klein bottle is named after the German mathematician Felix Klein (1849-1925). Compare Möbius strip.