# Does every closed curve contain the vertices of a square?

This is the question on Futility Closet

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See here. –  Ragib Zaman Mar 23 '12 at 9:07
@RagibZaman thanks –  yiyi Mar 23 '12 at 9:12
The question is essentially settled for $C^2$ curves, locally graphical curves if we restrict ourselves to one codimension. There is still more to be done (rectifiable curves would be interesting). –  Glen Wheeler Mar 23 '12 at 9:15
Another place to look would be Jason Cantarella's page on the topic jasoncantarella.com/webpage/index.php?title=Square_Peg_problem –  Louis Mar 23 '12 at 10:46

So it is true for e.g. all piecewise smooth curves, which are the kind we tend to imagine. Stromquist more generally implies an affirmative answer for curves that are piecewise graphs (as in $y=f(x)$) of continuous functions. Also see this page for further discussion.