John Sharp's Paradox:
How Is It Possible?

The applet below illustrates a dissection akin to the ones of Curry, Hooper, Langman and Sam Loyd Son. John Sharp mentions it with a reference to his notes in an enlightening article, but demurs as to the source. Originally, a 13×13 square is cut into three pieces which, after a rearrangement appear to combine into an 8×21 rectangle - a loss of one square.

The puzzle is easily modified by changing the dimensions according to the properties of the Fibonacci sequence. Upon rearrangement of the pieces, a single square seems to intermittently appear or disappear.

As of March 2017, the last browser that ran Java applets stopped supporting Java plugins. As a shortcut, here's a combination grab of the applet main canvas:

John Sharp's paradox

What if applet does not run?

(The three pieces can be dragged from the square to the rectangle and backwards.)


  1. J. Sharp, Fraudulent dissection puzzles - a tour of the mathematics of bamboozlement, Mathematics in School, The Mathematical Association, September, 2002

Dissection Paradoxes

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