Square Peg Applet

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

The applet should be right here. You need to install or enable Java to see it. In the meantime here is a javascript version of it. It's considerably slower and loading and saving files is not possible.
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If the applet doesn't show, here is a tentative alternative.


Conjecture [Square Peg Problem (a.k.a. Inscribed Square Problem), Toepliz 1911]: Every continuous simple closed curve in the plane contains the four vertices of a square.

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.

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