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== Resolved cases ==
It is tempting to attempt to solve the inscribed square problem by [[mathematical proof|proving]] that a special class of well-behaved curves always contains an inscribed square, and then to approximate an arbitrary curve by a sequence of well-behaved curves and infer that there still exists an inscribed square as a [[limit (mathematics)|limit]] of squares inscribed in the curves of the sequence. One reason this argument has not been carried out to completion is that the limit of a sequence of squares may be a single point rather than itself being a square. Nevertheless, many special cases of curves are now known to have an inscribed square.<ref name="matschke">{{citation |last=Matschke |first=Benjamin |year=2014 |title=A survey on the square peg problem |journal=[[Notices of the American Mathematical Society]] |doi=10.1090/noti1100 |volume=61 |issue=4 |pages=346–352|doi-access=free |hdl=21.11116/0000-0004-15B8-5 |hdl-access=free }}</ref>
===Piecewise analytic curves===
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