123:, but no trace of it has been discovered in Greek literature. The earliest surviving mentions of it is are from the early 11th century, suggesting it was created in the late 10th or early 11th century. The name and its many variations are from Greek; it is unclear whether this was due to being created by a rare Western European with a classical education that involved learning Greek, or if the game had a genuine origin in Greece and the Greek-speaking
213:
246:
280:"49" square, a "36" triangle, a "25" triangle, and a "16" round, which adds up to the pyramid's value of 190. These irregular values make it hard for them to be captured by most of the capturing methods listed below, except for siege. Pyramids can move like a round, a triangle, or a square, as long as they still contain the respective piece, which makes them very valuable.
228:. It lost its popularity sharply in the 17th century, virtually disappearing as the style of teaching mathematics changed, and Boethius's mathematics was considered old-fashioned and obsolete. One issue was that the rules were never standardized, with major variations from teacher to teacher. The game partially survived by clinging to the now far more popular
158:. In the following centuries, Rithmomachia spread through schools and monasteries in the southern parts of Germany and France. It was used mainly as a teaching aid, but gradually intellectuals started to play it for pleasure. In the 13th century Rithmomachia came to England, where famous mathematician
279:
Pyramids: Pyramids are not actually one piece, but more than one piece put together. The white pyramid is made of a "36" square, a "25" square, a "16" triangle, a "9" triangle, a "4" round, and a "1" round, which totals up to the pyramid's value of 91. The black pyramid is made up of a "64" square, a
338:
de honore liteque ("by honour and lawsuit"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, the number of digits in their captured pieces' values are less than a number set by both players, and the number of pieces they captured are less than a
253:
Rithmomachia is played on a board resembling the one used for chess or checkers with eight squares on the shorter side, but with sixteen on the longer side. The forms used for the pieces were triangles, squares, and rounds. Pyramids could be formed by stacking pieces. The game was noteworthy in that
312:
There were also a variety of victory conditions for determining when a game would end and who the winner was. There were common victories, and proper victories, which were recommended for more skilled players. Proper victories required placing pieces in linear arrangements in the opponent's side of
236:
included the rules of rithmomachia as an appendix in one of his books on chess, and the game persisted as "arithmetic chess" or "numerical checkers" as a side mention in German chess books for some time afterward, a curiosity but a rarely-played one. The game was rediscovered in the 20th century by
176:
play it for recreation. The game was known well enough to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century. Two notices advertising a game set for sale have been found, one in Paris (1556) and the other in London (1563). Nevertheless, no archaeological
75:
mathematical philosophy, which emphasized the natural harmony and perfection of number and proportion, that it was used both as a mnemonic drill for the study of
Boethian number theory and, more importantly, as a vehicle for moral education, by reminding players of the mathematical harmony of
257:
The rules below describe the most common version of the game, played through much of the Middle Ages and
Renaissance. There was also a variant propounded by Fulke in the 16th century, with significantly different (and somewhat more consistent) capture rules.
70:
to those in
Western Europe who received a classical education during the medieval period. David Sepkoski wrote that between the twelfth and sixteenth centuries, "rithmomachia served as a practical exemplar for teaching the contemplative values of
313:
the board, with the numbers formed by the arrangement following various types of numerical progression. The types of progression required — arithmetic, geometric and harmonic — fit with the mathematical and numerological teachings of
Boethius.
330:
De lite ("by lawsuit"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of digits in their captured pieces' values are less than a number set by both players, they win the
57:, and other variants) is an early European mathematical board game. Its earliest known description dates from the eleventh century. The name comes loosely from Greek and means "The Battle of the Numbers." The game is somewhat like
334:
De honore ("by honour"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, and the number of pieces they captured are less than a certain number set by both players, they win the
194:
The most ancient and learned Playe, called the
Philosopher's Game invented for the honest recreation of Students and other sober persons, in passing the tedious of tyme to the release of their labours, and the exercise of their
145:
was the standard textbook for instruction in arithmetics in the period for those lucky enough to receive a medieval education. The rules of the game were improved and spelled out more shortly thereafter by another monk,
27:
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the black and white forces were not symmetrical. Although each side had the same array of pieces, the numbers on them differed, allowing different possible captures and winning configurations to the two players.
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Ambuscade: If two pieces' sum is equal to an enemy piece that is placed between the two (i.e. the enemy piece is within a move of both attacking pieces), the enemy piece is captured and removed from the
354:
Victoria major ("greater victory"): This occurs when four pieces that are arranged have three pieces that are in a certain progression, and another three pieces that are in another type of progression.
289:
There were a variety of capture methods. Pieces do not land on another piece to capture it, but instead remain in their square and remove the other. If a piece is captured, it changes sides.
76:
creation." The game declined sharply in popularity in the 17th century, as it was no longer used in education, and potential players were not introduced to it during their schooling.
296:
Assault: If a piece with a small value, multiplied by the number of vacant spaces between it and another larger piece is equal to the larger piece, the larger piece is captured.
357:
Victoria excellentissima ("most excellent victory"): This occurs when four pieces that are arranged have all three types of mathematical progressions in three different groups.
293:
Meeting: If a piece could capture another piece with the same value by landing on it, the piece stays in its location and the opponent's piece is taken from the board.
503:
Ortografia
Enciclopedica Universale Della Lingua Italiana: PO - R; Con Appendice. 2,6 : Dizionario Enciclopedico Delle Scienze, Lettere Ed Arti
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De bonis ("by goods"): If a player captures enough pieces to add up to or exceed a certain value that is set by both players, they win the game.
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evidence of the game (such as playing boards) has survived from the medieval and early modern periods, in contrast to many other board games.
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Sir
Rowland Hill's headquarters in Shropshire: the tiled floor of a basement room contains a 16th century Rithmomachia board
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The first written evidence of
Rithmomachia dates to around 1030, when a monk named Asilo (probably the future Bishop
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The game was used as an educational tool that teachers could introduce while teaching arithmetic as part of the
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348:
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David
Sepkoski, "Ann E. Moyer: The Philosopher’s Game: Rithmomachia in Medieval and Renaissance Europe.”
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324:: "by body"): If a player captures a certain number of pieces set by both players, they win the game.
147:
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Vestigia mathematica: Studies in
Medieval and Early Modern Mathematics in Honour of H.L.L. Busard
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Triangles: Triangles can move exactly two squares vertically or horizontally, but not diagonally.
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Squares: Squares can move exactly three squares vertically or horizontally, but not diagonally.
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Victoria magna ("great victory"): This occurs when three pieces that are arranged are in an
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Literatur des Schachspiels, [a bibliogr.] gesammelt, geordnet und mit Anmerkungen
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Ann E. Moyer, "The Philosopher's Game: Rithmomachia in Medieval and Renaissance Europe."
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A World of Chess: Its Development and Variations Through Centuries and Civilizations
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except that most methods of capture depend on the numbers inscribed on each piece.
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Little is known about the origin of the game. Medieval writers attributed it to
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Rithmomachia was at its most popular in the 16th century. The Tudor polymath,
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There are four types of pieces: Rounds, Triangles, Squares, and Pyramids.
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1554 illustration of a Rithmomachy board and pieces by Claude de Boissière
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The Most Noble, ancient and learned playe, called the Philosopher's Game
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The Philosopher's Game: Rithmomachia in Medieval and Renaissance Europe
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400:, battles. So a literal translation might be "Number-Rhythm Battles".
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A translation of the rules established by Claude de Boissière in 1556
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Stigter, Jurgen (2007). "Rithmomachia, the Philosopher's Game". In
460:, Vol. 95, No. 4 (December 2004), pp. 697–699. David Seposki
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published a version in Venice which was translated into German by
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Siege: If a piece is surrounded on all four sides, it is removed.
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Rounds: Rounds move one square in any of the four diagonals.
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Strutt's Sports & Pastimes of the People of England
134:) created a game that illustrated the number theory of
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Rules for the Fulke's 16th century variant of the game
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certain number set by both players, they win the game.
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William Fulke (1563), translating Boissiere (1556),
532:. Mathematical Association of America. p. 144.
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Fulke, "Of these partes in the fyrst kynd of playng"
686:, Vol. 95, No. 4 (December 2004), pp. 697–699.
201:also contains a board for the game on a basement
166:recommended Rithmomachia to his students, while
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436:. The British Museum Press. pp. 263–269.
237:historians of board games such as Arno Borst.
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473:(University of Michigan Press, 2001), p. 20.
621:Die «Rithmachia» des Werinher von Tegernsee
714:Medieval & Renaissance Games Home Page
170:let the inhabitants described in the book
141:, for the students of monastery schools.
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192:, published on the game under the title
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603:Numerology, or What Pythagoras Wrought
584:Jean-Louis Cazaux and Rick Knowlton,
572:Das mittelalterliche Zahlenkampfspiel
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623:, in M. Folkerts - J. P. Hogendijk,
721:— modern version of the rules (rus)
607:Mathematical Association of America
376:The first word is a combination of
689:Joseph Strutt and J. Charles Cox,
627:, Amsterdam 1993, pp. 107–142
434:Ancient Board Games in Perspective
89:Which dulle wittits dothe encombre
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670:The Oxford History of Board Games
529:Mathematics in Historical Context
506:(in Italian). Bazzarini, Antonio.
91:For thys play stant al by noumbre
658:, University of Michigan Press,
112:Earliest known English reference
21:The Philosophers' Football Match
489:(in German). Oxford University.
226:Augustus II, Duke of Brunswick
87:The play he can of Ryghtmadhye
1:
605:, Chapter 17, "Rithmomachy",
392:, rhythm; the second word is
644:, pp. 201 & 598-9,
642:Histoire des jeux de société
162:wrote a text about it. Even
101:By thise Philosophurs olde.
500:Bazzarini, Antonio (1834).
143:De institutione arithmetica
139:De institutione arithmetica
93:And hath al his conclusions
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249:Hand-made Rithmomachy set
99:As hyt ys in remembraunce
745:Traditional board games
735:Abstract strategy games
154:, and in the school of
114:to Rithmomachia, ~1407.
109:Reson & Sensuallyte
16:Mathematical board game
740:History of board games
656:The Philosopher's Game
349:arithmetic progression
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197:in 1562; his house at
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97:By so sotil ordynaunce
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526:Suzuki, Jeff (2009).
483:Anton Schmid (1847).
248:
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184:and publisher of the
95:Chefly in proporsions
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672:, pp. 332–342,
636:Online transcription
148:Hermannus Contractus
132:Adalbero of Würzburg
19:For other uses, see
750:Mathematical games
719:Ритмомахия «ASILO»
640:Jean-Marie Lhôte,
558:The Boardgame Book
344:Proper victories:
317:Common victories:
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218:
160:Thomas Bradwardine
107:John Lydgate,
55:philosophers' game
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539:978-0-88385-570-6
430:Finkel, Irving L.
222:Francesco Barozzi
150:(1013–1054) from
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693:, pp. 254–5
619:Menso Folkerts,
599:Underwood Dudley
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51:rhythmomachy
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35:Rithmomachia
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207:prayer room
164:Roger Bacon
47:rythmomachy
39:rithmomachy
729:Categories
408:References
121:Pythagoras
67:quadrivium
285:Capturing
182:statesman
152:Reichenau
136:Boethius'
382:arithmós
241:Gameplay
220:In 1572
73:Boethian
432:(ed.).
390:rythmós
378:αριθμός
308:Victory
203:parlour
80:History
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398:máchia
386:ρυθμός
300:board.
262:Pieces
195:Wittes
173:Utopia
53:, the
394:μάχια
364:Notes
335:game.
331:game.
322:Latin
230:chess
156:Liège
59:chess
684:Isis
674:ISBN
660:ISBN
646:ISBN
611:ISBN
590:ISBN
576:ISBN
562:ISBN
534:ISBN
458:Isis
438:ISBN
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
