is there a simple Jordan closed curve that has 4 points which can not form a rectangle? how about 3 dimension?
does every simple Jordan closed curve has Inscribed rectangle?
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$\begingroup$
geometry
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1Here's a cool video exploring that problem: https://www.youtube.com/watch?v=AmgkSdhK4K8 – 2017-02-01
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0And here's an article (Theorem 7, pgs 7-8): http://people.mpim-bonn.mpg.de/matschke/SurveyOnSquarePeg_extension14.pdf – 2017-02-01