Mathematical dissection

In mathematics, dissection is cutting apart one or more figures and rearranging the pieces to make another figure. Dissection puzzles have been around for thousands of years. The problem of dissecting two equal squares to form one larger square using four pieces dates back to at least the time of Plato (427–347 BC). In the 10th century, Arabian mathematicians described several dissections in their commentaries on Euclid's Elements. The 18th-century Chinese scholar Tai Chen presented an elegant dissection for approximating the value of pi. Others worked out dissection proofs of Pythagorean theorem.


In the 19th century, dissection puzzles by Sam Loyd, Henry Dudeney, and others became tremendously popular in magazine and newspaper columns. A classic example is the haberdasher's puzzle. Dissections can get quite elaborate: an eight-piece octahedron becomes a hexagon, a nine-piece five-pointed star becomes a pentagon, and so on.


See also:


Blanche's dissection
cake-cutting, or fair division
Hadwiger problem
loculus of Archimedes
Mrs. Perkins' quilt
Pythagorean square puzzle



1. Lindgren, Harry. Geometric Dissections. New York: Van Nostrand Reinhold, 1964.
2. Lindgren, Harry. Recreational Problems in Geometrical Dissections and How to Solve Them. New York: Dover Publications, 1972.
3. Frederickson, Greg N. Dissections: Plane and Fancy. Cambridge: Cambridge University Press, 1997.