In ancient Greek geometry, the Ostomachion, also known as () or syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and a copy, the Archimedes Palimpsest, of the original ancient Greek text made in Byzantine times.Darling, David (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley and Sons, p. 188.
The word Ostomachion ()ὀστομάχιον, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library comes .ὀστέον, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Libraryμάχη, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library The manuscripts refer to the word as "Stomachion", an apparent corruption of the original Greek. Ausonius 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.Ausonii Cento nuptialis in Monumenta Germaniae Historica, auctores antiquissimi, vol. 5, part 2: D. Magni Ausonii opuscola, Berolini apud Weidmannos, 1883, pagg. 140-41 . It is not known which is older, Archimedes' geometrical investigation of the figure, or the game. Victorinus,Ars grammatica, III, 1 in Grammatici latini, Lipsiae in aedibus R. G. Teubneri, 1857, vol. 6, part 1, pagg. 100-01. Bassus,De metris, 9 in Grammatici latini cit., pagg. 271-72, EnnodiusCarmen CCCXL (2, 133) in Monumenta Germaniae Historica, auctores antiquissimi, vol. 7, Magni Felicis Ennodi opera, Berolini apud Weidmannos, 1885, pag. 249 and LucretiusDe rerum natura, II, 776-787 cited in 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.
The number of different ways to arrange the parts of the Ostomachion 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. 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
Further reading 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
Heinrich Suter, Loculus James Gow, Short History W. W. R. Ball, Recreations and Essays The Ostomachion at the Bibliotheca Augustana 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 than 7,300 shapes proposed by the program.