# 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 tenth century, Arabian mathematicians
described several dissections in their commentaries on Euclid's *Elements*.
The eighteenth-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 nineteenth 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

T-puzzle

### References

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.