*Ostomachion*

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* Ostomachion*, also known as

*(Archimedes' box in Latin) and also as*

**loculus Archimedius***, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and a copy, the*

**syntomachion***Archimedes Palimpsest*, of the original ancient Greek text made in Byzantine times.

^{[1]}The word Ostomachion has as its roots in the Greek Ὀστομάχιον,

^{[2]}which means "bone-fight", from ὀστέον (

*osteon*), "bone"

^{[3]}and μάχη (

*mache*), "fight, battle, combat".

^{[4]}Note that the manuscripts refer to the word as "

**Stomachion**", an apparent corruption of the original Greek. Ausonius 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 tangrams and was played perhaps by several persons with pieces made of bone.

^{[5]}It is not known which is older, Archimedes' geometrical investigation of the figure, or the game. Victorinus,

^{[6]}Bassus

^{[7]}Ennodius

^{[8]}and Lucretius

^{[9]}have talked about the game too.

## Game[edit]

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, Susan P. Holmes, and Ronald Graham, and confirmed by a computer search by William H. Cutler.^{[10]}
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.^{[11]}

## References[edit]

**^**Darling, David (2004).*The universal book of mathematics: from Abracadabra to Zeno's paradoxes*. John Wiley and Sons, p. 188. ISBN 0-471-27047-4**^**ὀστομάχιον, Henry George Liddell, Robert Scott,*A Greek-English Lexicon*, on Perseus Digital Library**^**ὀστέον, Henry George Liddell, Robert Scott,*A Greek-English Lexicon*, on Perseus Digital Library**^**μάχη, Henry George Liddell, Robert Scott,*A Greek-English Lexicon*, on Perseus Digital Library**^**Ausonii*Cento nuptialis*in*Monumenta Germaniae Historica*, auctores antiquissimi, vol. 5, part 2: D. Magni Ausonii opuscola, Berolini apud Weidmannos, 1883, pagg. 140-41.**^**Ars grammatica, III, 1 in*Grammatici latini*, Lipsiae in aedibus R. G. Teubneri, 1857, vol. 6, part 1, pagg. 100-01.**^**De metris, 9 in*Grammatici latini*cit., pagg. 271-72,**^***Carmen CCCXL (2, 133)*in*Monumenta Germaniae Historica*, auctores antiquissimi, vol. 7, Magni Felicis Ennodi opera, Berolini apud Weidmannos, 1885, pag. 249**^***De rerum natura*, II, 776-787 cited in Reviel Netz, Fabio Acerbi, Nigel Wilson (2004). "Towards a reconstruction of Archimedes' Stomachion" (PDF).*SCIAMVS*.**5**: 67–99. Retrieved 3 October 2013.CS1 maint: multiple names: authors list (link)**^**Kolata, Gina (December 14, 2003), "In Archimedes' Puzzle, a New Eureka Moment",*The New York Times***^**Huxley, G. L. (Winter 2009), "Review of*Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic*",*Hermathena*,**187**: 116–121, JSTOR 23317530

## Further reading[edit]

- J. L. Heiberg, Archimedis opera omnia, vol. 2, pp. 420 ff., Leipzig: Teubner 1881
- Reviel Netz & William Noel,
*The Archimedes Codex*(Weidenfeld & Nicolson, 2007) - J. Väterlein, Roma ludens (Heuremata - Studien zu Literatur, Sprachen und Kultur der Antike, Bd. 5), Amsterdam: Verlag B. R. Grüner bv 1976

## External links[edit]

Wikimedia Commons has media related to .Stomachion |

- Heinrich Suter, Loculus
- James Gow, Short History
- W. W. R. Ball, Recreations and Essays
- Ostomachion, a Graeco-Roman puzzle
- Professor Chris Rorres
- Kolata, Gina. "In Archimedes' Puzzle, a New Eureka Moment."
*The New York Times*. December 14, 2003 - A tour of Archimedes' Stomachion, by Fan Chung and Ronald Graham.
- Ostomachion and others tangram Play with 38 Tangram games online: more that 7,300 shapes proposed by the program.