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The Inscribed Square Problem, also known as Toeplitz’ conjecture or the square peg problem, as stated on wikipedia asks:

Does every plane simple closed curve contain all four vertices of some square?

With a few examples, we can begin to get a sense of where squares show up on their respective paths. Though, after seeing some of these images I wanted to get a better sense of what features of a path allow squares to attach all their vertices to it thus being a path for which the conjecture holds true.

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About

Jens Vyff

Enjoys ideas and their exploration

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