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Who cares about topology? (Inscribed rectangle problem)

An unsolved conjecture, and a clever topological solution to a weaker version of the question.
Brought to you by you: http://3b1b.co/topology-thanks
Home page: https://www.3blue1brown.com/

This video is based on a proof from H. Vaughan, 1977.

You can see it written up (as a single rather-dense paragraph) here:
http://topo.math.auburn.edu/tp/reprints/v06/tp06107.pdf

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