Recreational Math

Math Puzzles

What is a stomachion?

A stomachion is a dissection puzzle similar to a Tangram. It uses 14 pieces in the puzzle, each of varying polygonal shapes and arranged into a 12 by 12 square grid. Each of the pieces has an area that is an integral fraction: for example, 24, 12, 9, 6, or 3, of the total area of the square, which is 144 units. The object of a stomachion is to arrange the pieces into interesting, and often recognizable shapes, such as people, animals, and objects.

This puzzle was also an ancient game known to the Greek mathematician Archimedes (c. 287-212 B.C.E.), and thus is also called the Loculus of Archimedes (“Archimedes Box”). It is doubtful Archimedes invented the puzzle, but he did explore its geometric aspects. It also now appears that in contemplating the different solutions to this puzzle, Archimedes actually was anticipating the branch of mathematics we now call combinatorics.


This is an example of a stomachion, a type of puzzle in which a geometric shape is dissected into several smaller shapes that can then be rearranged.


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