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.

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

References

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

Dissection Paradoxes

• Curry's Paradox
• Dissection of a 10×13 Rectangle into Two Chessboards
• A Faulty Dissection
• Hooper's Paradox
• John Sharp's Paradox
• Langman's Paradox
• Popping A Square
• Sam Loyd's Son's Dissection

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