Inscribing Rectangles in Jordan Loops
Inscribing Rectangles in Jordan Loops
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Richard Schwartz, Brown University
I'll show a graphical user interface IÌýwrote which explores the problem of inscribing rectanglesÌýin Jordan loops.ÌýThe motivation behind this is theÌýnotorious Square Peg Conjecture of Toeplitz, from 1911.ÌýI did not manage to solve this problem, but I did getÌýthe result that at most 4 points of any Jordan loop areÌývertices of inscribedÌý rectangles. I will sketch a proofÌýof this result, mostly through visual demos, and also IÌýwill explain two other theorems about inscribed rectanglesÌýwhich at least bear a resemblance to theorems in symplecticÌýgeometry.