Klein Bottle
/klaɪn ˈbɒtəl/noun
A one-sided mathematical surface with no distinct inside or outside, often represented as a bottle whose neck passes through its side and joins its base.
Did you know?A true Klein bottle cannot be constructed in ordinary three-dimensional space without its surface intersecting itself; it can exist without self-intersection in four dimensions.
Etymological Timeline
Proto-Germanic
Proto-Germanic
*klainiz
“Small or slender; the ancestral source of German klein.”
Old High German
Old High German
kleini
“Small, delicate, or fine.”
Modern German
German
klein
“Small; used in the surname of mathematician Felix Klein.”
1882
German
Kleinsche Fläche
““Klein surface,” Felix Klein’s term for the non-orientable surface later associated with the bottle-shaped model.”
Late 19th Century
English
Klein bottle
“The English name formed by combining Klein’s surname with bottle, referring to the surface’s visual bottle-like representation.”
Modern English
English
Klein bottle
“A closed, one-sided surface with no boundary and no separable interior or exterior.”