Ostomachion

Stomachion ( altgr. Στομάχιον ), actually Ostomachion ( Ὀστομάχιον ), is the title of a mathematical signature of Archimedes, which is only fragmentarily preserved in two manuscripts, an Arabic translation and in the original Greek from a Byzantine manuscript from the 10th century (so-called Palimpsest of Archimedes ).

Probably to " Stomachion " mutilated by the Arab tradition word is called the Roman writer Ausonius correct " Ostomachion " ( " quod Graeci ostomachion vocavere " " what the Greeks call Ostomachion " ), as the Danish Archimedesforscher Johann L. Heiberg in his edition of the fragment was able to show. Etymologically results in either the meaning " bone - competition " (from the Greek osteon bone ὀστέον, leg and μάχη mâché battle, fight ) or "neck- game" (from Latin stomachari get angry, stomachus stomach, but also resentment, anger, resentment, indignation, cf Greek στόμαχος stomachos stomach).

Archimedes describes in his work a puzzle, can be placed on the ivory plate characters from 14 initially arranged in a square, and analyzes the combinatorial possibilities, in how many ways the square can be put.

It is not known and can thus probably not clarify whether Archimedes designed the game itself or dealt only with the geometrical problems of the existing puzzles.

The game

The Stomachion, also known as " Loculus Archimedius " or in English under the name " elephant puzzle," is a Chinese tangram -like layers and patience. The basic pattern consists of 14 three-, four -and five corners, which can be put together in different ways to form a square.

The aim of the game is going to give interesting as possible figures that are reminiscent of familiar shapes, such as animals, people or objects. For example, the late ancient Roman statesman and poet Ausonius and other ancient writers mention the following figures you can lay out the 14 parts: a helmet, a flying goose, a tower, a column, an elephant, a boar, a barking dog, a lurking hunter, a gladiator. This happened probably in a kind of competition with two or more players.

The mathematical problem

The number of different ways to arrange the parts of the Stomachions within a square, were determined in 2003 at the suggestion of the American historian of science Reviel and William Noel of four mathematicians in six weeks using a computer program to a total of 17,152; this maximum number can be but if you do not count reflections and rotations, reduce to 536.