Inscribed Square Problem
A Jordan curve is a continuous function from the closed interval to the plane with the properties that is injective on the half-open interval (i.e., is simple) and (i.e., is closed).
[M] Meyerson, M.D., Equilateral triangles and continuous curves, Fund. Math. 110, (1980), 1--9.
* indicates original appearance(s) of problem.