The rectangular peg theorem states that, for every smooth Jordan curve in the Euclidean plane and every rectangle 
, the curve contains four points
that are the vertices of a rectangle similar to 
(Greene and Lobb 2021). Taking 
to be a square
gives the smooth case of the square peg problem.
The prescribed rectangle may have any aspect ratio. Thus the result is stronger than merely finding some rectangle or some square on the curve.
