''Ostomachion'', also known as ''loculus Archimedius'' (Archimedes' box in

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

) and also as ''syntomachion'', is a mathematical treatise attributed to

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

. This work has survived fragmentarily in an

Arabic Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...

version and a copy, the ''

Archimedes Palimpsest The Archimedes Palimpsest is a parchment codex palimpsest, originally a Byzantine Greek copy of a compilation of Archimedes and other authors. It contains two works of Archimedes that were thought to have been lost (the ''Ostomachion'' and the ' ...

'', of the original

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

text made in

Byzantine The Byzantine Empire, also referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire primarily in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinopl ...

times.Darling, David (2004). ''The universal book of mathematics: from Abracadabra to Zeno's paradoxes''. John Wiley and Sons, p. 188. The word Ostomachion has as its roots in the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

Ὀστομάχιον, which means "bone-fight", from ὀστέον (''osteon''), "bone" and μάχη (''mache''), "fight, battle, combat". Note that the manuscripts refer to the word as "Stomachion", an apparent corruption of the original Greek.

Ausonius Decimius Magnus Ausonius (; – c. 395) was a Roman poet and teacher of rhetoric from Burdigala in Aquitaine, modern Bordeaux, France. For a time he was tutor to the future emperor Gratian, who afterwards bestowed the consulship on him. H ...

gives us the correct name "Ostomachion" (''quod Graeci ostomachion vocavere,'' "which the Greeks called ostomachion"). The Ostomachion which he describes was a puzzle similar to

tangram The tangram () is a dissection puzzle consisting of seven flat polygons, called ''tans'', which are put together to form shapes. The objective is to replicate a pattern (given only an outline) generally found in a puzzle book using all seven pie ...

s 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 Marcus Piavonius VictorinusSome of the inscriptions record his name as M. Piavvonius Victorinus, as does the first release of coins from the Colonia mint. A mosaic from Augusta Treverorum (Trier) lists him as Piaonius. was emperor in the Gallic ...

, Bassus Ennodius and

Lucretius Titus Lucretius Carus ( , ; – ) 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, and which usually is translated into E ...

have talked about the game too.

Game

The game is a 14-piece

dissection puzzle A dissection puzzle, also called a transformation puzzle or ''Richter Puzzle'', is a tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes. The creation of new dissection puzzles ...

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 Fan-Rong King Chung Graham (; born October 9, 1949), known professionally as Fan Chung, is a Taiwanese-born American mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in g ...

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

and

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

Game

References

Further reading

External links