In ancient Greek geometry, the ''Ostomachion'', also known as () or ''syntomachion'', is a mathematical treatise attributed to

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...

. This work has survived fragmentarily in an

Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...

version and a copy, the '' Archimedes Palimpsest'', of the original

ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...

text made in

Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...

times.Darling, David (2004). ''The universal book of mathematics: from Abracadabra to Zeno's paradoxes''. John Wiley and Sons, p. 188. The word ''Ostomachion'' () comes . The manuscripts refer to the word as "Stomachion", an apparent corruption of the original Greek.

Ausonius Decimius Magnus Ausonius (; ) was a Latin literature, Roman poet and Education in ancient Rome, teacher of classical rhetoric, rhetoric from Burdigala, Gallia Aquitania, Aquitaine (now Bordeaux, France). For a time, he was tutor to the future E ...

gives us the correct name "Ostomachion" (, "which the Greeks called ostomachion"). The ''Ostomachion'' which he describes was a puzzle similar to tangrams and was played perhaps by several persons with pieces made of bone. It is not known which is older, Archimedes' geometrical investigation of the figure, or the game. Victorinus, Bassus Ennodius and

Lucretius Titus Lucretius Carus ( ; ; – October 15, 55 BC) was a Roman poet and philosopher. His only known work is the philosophical poem '' De rerum natura'', a didactic work about the tenets and philosophy of Epicureanism, which usually is t ...

have also discussed the game.

Game

The game is a 14-piece dissection puzzle forming a square. One form of play to which classical texts attest is the creation of different objects, animals, plants etc. by rearranging the pieces: an elephant, a tree, a barking dog, a ship, a sword, a tower etc. Another suggestion is that it exercised and developed memory skills in the young. James Gow, in his ''Short History of Greek Mathematics'' (1884), footnotes that the purpose was to put the pieces back in their box, and this was also a view expressed by W. W. Rouse Ball in some intermediate editions of ''Mathematical Essays and Recreations'', but edited out from 1939. The number of different ways to arrange the parts of the Stomachions within a square were determined to be 17,152 by Fan Chung,

Persi Diaconis Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known f ...

, Susan P. Holmes, and

Ronald Graham Ronald Lewis Graham (October 31, 1935July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He ...

, and confirmed by a computer search by William H. Cutler. However, this count has been disputed because surviving images of the puzzle show it in a rectangle, not a square, and rotations or reflections of pieces may not have been allowed.

References

External links

Heinrich Suter, LoculusJames Gow, Short HistoryW. W. R. Ball, Recreations and Essays
* ttp://math.ucsd.edu/~fan/stomach/ A tour of Archimedes' Stomachion by Fan Chung and

.
Ostomachion and others tangram
Play with 38 Tangram games online: more than 7,300 shapes proposed by the program. {{Ancient Greek mathematics Puzzles Tiling puzzles Works by Archimedes Geometric dissection

Game

References

Further reading

External links