I have a question. I recently came across the inscribed square problem as one that - to date - is unsolved. However all of the picture I see of examples of this show a closed loop with edges which cross over the closed loop. My understanding of the term inscribed means that the vertices AND the sides of the square are inside the figure. If the figures were all 'inscribed' it seems rather obvious that all closed loops can contain atleast one square. Is there something I am missing here?
2026-05-16 13:01:11.1778936471
inscribed square problem
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The definition of inscribed in the problem is not what you are thinking. The problem only asks that there be four points on the curve that form the vertices of a square. The sides of the square are allowed to pass outside the curve as shown in the figure from Wikipedia. The article is explicit about the fact that the sides may go outside the curve and the vertices may not be visited in order along the curve. Even so, this version of inscribed just gives more freedom than the version you were thinking of. Why do you think the harder one is obvious?