Klein bottle
- noun
- Specialized
:
botella de Klein
- Mathematicians often use the Klein bottle to demonstrate concepts related to non-orientable surfaces.
I want to push out Klein bottles as a secret sign inside of rap videos in hip hop, right?
- I want to push out Klein bottles as a secret sign inside of rap videos in hip hop, right?
Examples
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I want to push out Klein bottles as a secret sign inside of rap videos in hip hop, right?
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Yes, you can fill a Klein bottle with water.
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In the case of the Klein bottle, neck extends out from the bottle, turns around, goes back in.
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Now I would like to make better Klein bottles of a higher genus.
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The problem that we have is that it intersects itself, and a real Klein bottle doesn't intersect itself.
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OK, so as much as Mobius stripes and Klein bottles are exciting and really cool, well we can't use them in this class because we can't define flux for them.
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A Klein bottle is a fascinating object in topology that has only one side and no boundary.
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To visualize a Klein bottle, imagine a tube that loops back through itself in a continuous surface.
Surface Forms
Morphology
Klein + bottle
The term combines a proper name ('Klein') with a common noun ('bottle'), but the technical topological meaning (a one-sided closed surface) is not derivable from either part; 'bottle' only suggests an ordinary container and the name gives no semantic cue. This is a specialized mathematical concept whose meaning is idiomatic/technical rather than compositional, so a B1 learner knowing the constituents would not be able to infer the full meaning.
Etymology
Klein bottle is named after the mathematician Felix Klein, but the easy picture is a glass bottle whose neck is pushed through its side and joined to the bottom. Because of this joining, the inside and outside become one continuous surface, so a Klein bottle is a shape with 'only one side' and 'no edge'.
