The discrete square peg problem

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Pak, Igor
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Abstract
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The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, but remains open in full generality. We present two new direct proofs for the case of piecewise linear curves.
Keywords
Mathematics - Metric Geometry, Mathematics - Combinatorics, 53A04, 52C99
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