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EebstertheGreat
Numberphile
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Comments by "EebstertheGreat" (@EebstertheGreat) on "The Girl with the Hyperbolic Helicoid Tattoo - Numberphile" video.
Pairs of pants are exactly what you would expect them to be. They have three holes, like a pair of pants.
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Topologically speaking, a pair of pants is homeomorphic to the sphere with three holes. That's actually the definition of a pair of pants.
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@thesuccessfulone A pair of pants has three holes: one for each leg, and one for the waist. What one-hole pants are you talking about?
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@thesuccessfulone It's really not a misnomer. A pair of pants has three holes in it. A pipe has two holes. This seems like the most straightforward way to describe it. Remember that in topology, two surfaces are isomorphic (essentially the same) if you can continuously deform one into the other. So you can move around the holes. Clearly a pair of pants has three of them to move around.
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@rstriker21 I don't understand what you mean. How do you consider a pair of pants "as a volume"?
1