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Pick’s Theorem

Two manuscripts in fragmentary form attributed to Archimedes survive on an ancient game that the Greeks called the Stomachion (Στομάχιον). One is an Arabic translation and the other is a Greek manuscript dating from the tenth century discovered in Constantinople in 1899. It is not known whether Archimedes invented the game (probably not) or simply explored the geometrical aspects of the game (more probable). There are many other references to the game in the ancient literature, of which two refer to it in Latin as loculus Archimedius (Archimedes’ box). The word Stomachion has as its root the Greek word for stomach (στόμαχος), but otherwise its meaning is unclear.

The game consisted of 14 flat ivory pieces of various polygonal shapes originally forming a square. The object of the game was to rearrange the pieces to form interesting things (people, animals, objects, etc.) such as the elephant(?) on the right. This elephant is from a manuscript of Ausonius (a Roman poet and statesman of the fourth century A.D.) who compares the Stomachion to a form of poetry in which various meters are jumbled together.

The Greek manuscript attributed to Archimedes is rather incomplete and is concerned with determining the relationships of various angles of the pieces. The Arabic manuscript provides more information, describing a construction of the Stomachion and determining the areas of its pieces.