Square Peg Applet

(a.k.a. the Inscribed Square Applet)

The applet should be right here. You must install or enable Java to see it.

If the applet doesn't show, here is a tentative alternative.

The Square Peg Problem is only know to hold true for curves that are "smooth enough", e.g. C¹-curves do it. Many proofs for different curve classes are known.

Conjecture [Rectangular Peg Problem]: Every smooth simple closed curve in the plane contains the four vertices of a rectangle with a prescribed aspect ratio r:1.

The Rectangular Peg Problem (for smooth curves) is only known to hold true for r=1, that is, for squares.

Links:

• More software and animations by Jason Cantarella.
• Blog post on the history by Elizabeth Denne.
• A recent survey article by myself.