klein bottle in English

noun
1
a closed surface with only one side, formed by passing one end of a tube through the side of the tube and joining it to the other end.
Gluing the top of the Möbius band to the bottom would give you a compact Klein bottle , a complicated shape that is impossible to draw properly in three dimensions.

Use "klein bottle" in a sentence

Below are sample sentences containing the word "klein bottle" from the English Dictionary. We can refer to these sentence patterns for sentences in case of finding sample sentences with the word "klein bottle", or refer to the context using the word "klein bottle" in the English Dictionary.

1. A closely related 'strange' geometrical object is the Klein bottle.

2. The following square is a fundamental polygon of the Klein bottle.

3. The common physical model of a Klein bottle is a similar construction.

4. The real projective plane, like the Klein bottle, cannot be embedded in three-dimensions without self-intersections.

5. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle.

6. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.

7. Six colors suffice to color any map on the surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four color theorem, which would require seven.