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Jan 16, 2018 at 5:23 comment added Martin Sleziak The link in eins6180 comment seems to be dead. I will add Internet Archive link and also link to A Survey on the Square Peg Problem on Notices website. Wikipedia article on this: Inscribed square problem.
Aug 10, 2016 at 10:46 comment added user80247 Thanks. I didn't know that this problem has a name.
Aug 10, 2016 at 10:11 comment added eins6180 Yes, see Matschke's survey. Search the document for "Inscribed rectangles".
Aug 10, 2016 at 10:02 history asked user80247 CC BY-SA 3.0