this post was submitted on 29 Oct 2023
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Ahhh yes. A pair of pants, any surface that is homeomorphic to a sphere with three holes.
I don't understand why the top image has 4 holes, when like you said pants only have 3 openings
the red lines indicate cuts
so on the left side, it displays two manners you could "make" pants from the forms presented. (the top series showing getting two pairs of pants from the one form and the bottom only getting one pair from the form)
the right side shows those same forms but with the cuts shifted along the surface in such a way that they are topologically similar (or something) in that they still maintain 3 holes. in essence, this image is stating that the shapes on the right are perfectly valid pants since they follow the same '3 hole rule' and are created from the same exact forms that create a universally recognized pair of pants.
Am I topological pants
Aren't pants a sphere with two holes? (A double torus?)
Edit: a 3d pair of pants is a double torus, a 2d one is a sphere with three holes