## 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.

What if applet does not run? |

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

### References

- 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

|Activities| |Contact| |Front page| |Contents| |Geometry| |Fallacies|

Copyright © 1996-2018 Alexander Bogomolny

66359911