The stomachion is a 14-piece dissection puzzle similar to tangrams. It is described in fragmentary manuscripts
attributed to Archimedes as noted by Magnus Ausonius (310-395 A.D.). The puzzle is
also referred to as the "loculus of Archimedes" (Archimedes' box) or "syntemachion"
in Latin texts. The word stomachion has as its root the Greek word , meaning "stomach."
Note that Ausonius refers to the figure as the "ostomachion," an apparent
corruption of the original Greek.
The puzzle consists of 14 flat pieces of various shapes arranged in the shape of a square, with the vertices of pieces occurring on a grid. Two pairs of pieces are
duplicated. Like tangrams, the object is to rearrange
the pieces to form interesting shapes such as the elephant illustrated above (Andrea).
Taking the square as having edge lengths 12, the pieces have areas 3, 3, 6, 6, 6, 6, 9, 12, 12, 12, 12, 12, 21, and 24, giving them relative areas 1, 1, 2, 2, 2, 2,
3, 4, 4, 4, 4, 4, 7, and 8. Interestingly, as noted by Coffin, it is always the case
that all polygons formed by connecting points on a regular square
grid must have areas in the ratios of whole numbers.
In November 2003, Bill Cutler found there to be 536 possible distinct arrangements of the pieces into a square, illustrated above, where solutions that are equivalent by rotation and reflection are considered identical (Pegg 2003).
, meaning "stomach."
Note that Ausonius refers to the figure as the "ostomachion," an apparent
corruption of the original Greek.
grid. Two pairs of pieces are
duplicated. Like tangrams, the object is to rearrange
the pieces to form interesting shapes such as the elephant illustrated above (Andrea).
McLeod, A. I. "Stomachion
of Archimedes."