{"id":328,"date":"2014-02-09T23:04:16","date_gmt":"2014-02-09T23:04:16","guid":{"rendered":"https:\/\/www.cescoreale.com\/?post_type=project&p=328"},"modified":"2026-06-11T07:18:23","modified_gmt":"2026-06-11T07:18:23","slug":"ludyssea-viaggio-matematico-tra-i-giochi-antichi","status":"publish","type":"project","link":"https:\/\/www.cescoreale.com\/eo\/project\/ludyssea-viaggio-matematico-tra-i-giochi-antichi\/","title":{"rendered":"Ludyssey – Mathematical journey through ancient games"},"content":{"rendered":"

[et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22″ background_color=”#8224e3″ global_colors_info=”{}”][et_pb_fullwidth_header title=”Ludyssey – Mathematical journey through ancient games” subhead=”Workshop – exhibition” content_max_width=”none” admin_label=”Fullwidth Header” _builder_version=”3.16″ background_color=”rgba(255, 255, 255, 0)” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”off” button_two_letter_spacing__hover_enabled=”off” button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.22″ global_colors_info=”{}”][et_pb_row column_structure=”3_4,1_4″ _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”3_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text admin_label=”Text” _builder_version=”3.27.4″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”]<\/p>\n

video Ludyssey<\/a><\/h2>\n

download the overview pdf: \u00a0Ludyssey- English<\/a><\/p>\n

“Consider the seed of your generation:
you were not made to live like brutes,
but to play games and make them science! “<\/p>\n

\"\"<\/a>Isn’t that what Dante’s Ulysses used to say in order to spur his fellow travelers (and players)?
In his wandering back and forth the Mediterranean horizons, Ludysseus was trying to trace the deep roots of the peoples through their games and the mathematics hidden therein. He analysed the game strategies, seeking and studying mathematically the game errors.
Ludyssey is a journey that takes you from the geometry of the Archimedean Ostomachion (square split into 14 different shapes) to the probability hidden in the variants of Backgammon (Ludus Duodecim Scriptorum for the Romans, Tavli for Greeks and Turks). From the periodic configurations of Mancaley (Syrian game of sowing) to the binomial law of Moroccan Sig, and finally to the arithmetic taught in medieval Italy and France through Rithmomachia, the “Battle of Numbers” (a kind of chess with sums and products).<\/p>\n

“And turning our stern toward morning,
we made wings of oars for our mad flight,
still playing chess and hide-and-seek”<\/p>\n

By Cesco Reale (Festival of Mathematical Games<\/a>). In collaboration with MateFitness<\/a> (CNR-PSC) and with CEMEA <\/a>Veneto.
Under the patronage of the Swiss Museum of Games<\/a> and with the financial support of Festival della Scienza<\/a>.<\/p>\n

WORKSHOP AND EXHIBITION
The animators illustrate the different games of Ludyssey and let people play, explaining the historical-cultural context where they are (or were) played and the general rules. Afterwards the public is invited to analyse some game situations that have links to mathematics: they will be asked to find the error in some movements or game configurations, and then to study the mathematical part that allows to correct the error. The activity is thought for schools and festivals, but also for a more demanding public, as it can be adapted to different levels. Moreover Ludyssey is also an exhibition, with panels to read and games to admire.<\/p>\n

Past events:<\/p>\n

–\u00a0Festival dellaScienza 2010, Genova<\/a><\/p>\n

–InfinitaMente\u00a02011,\u00a0\u00a0Univ.\u00a0Verona<\/a><\/p>\n

–\u00a0<\/a>SettimanadellaMatematica 2012, Univ. Brescia<\/a><\/p>\n

GAMES<\/p>\n

– Ostomachion. Pick’s theorem, which is the area of the following figures? Try to reproduce them with the game pieces. In how many ways can you rebuild the square? Computer animations of the possible square reconstructions and their graph.<\/p>\n

– Mancala. The remainder of the division. Which moves allow me to threaten a capture? Walking groups and periodic configurations. Ethno-mathematics: comparison between the analyses of mathematicians and local experts.<\/p>\n

– Sig: binary dice and binomial law. Video of Saharawi women playing in the desert.<\/p>\n

– Rithmomachia: presentation of Boethius\u2019 Arithmetica. Arithmetics, geometry and music in Pythagorean philosophy. Arithmetic, geometric and harmonic sequences.<\/p>\n

– Backgammon: comparison with the Ludus Duodecim scriptorum (ancient Roman game) and the modern versions in Greece; in this situation what is the best move to minimize the probability that the piece will be captured?<\/p>\n

MATERIALS. The exhibition consists of 10 panels (A1-size 84 x 60) and 20 wooden games used by the public during the workshops. Necessary space: 50-100 m2.<\/p>\n

References<\/strong><\/h1>\n

Mancala<\/h3>\n

– Marc Chemillier (Univ. Caen). El\u00e9ments pour une ethnomath\u00e9matique de l’aw\u00e9l\u00e9 (Mathematics and Social Sciences n. 181, 2008)
– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)
– Marino Carpignano (Progetto Abstrakta). http:\/\/www.pergioco.net\/Giochi\/GiochiDiTavoliere\/Mancala\/Mancala.htm
– http:\/\/www.awale.info
– Univ. Lisboa. Matem\u00e1tica em Jogo \u2014 exposi\u00e7\u00e3o virtual. http:\/\/mat.fc.ul.pt\/divulgacao\/mej\/expo_virtual<\/p>\n

Ostomachion<\/h3>\n

– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede.
http:\/\/areeweb.polito.it\/didattica\/polymath\/htmlS\/probegio\/GAMEMATH\/Stomachion\/Stomachion.htm
– Stomachion (Visualization of the 268 basic solutions) http:\/\/4umi.com\/play\/stomachion\/
Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion). http:\/\/www.math.ucsd.edu\/~fan\/stomach\/
– The Walters Art Museum. The story of the Archimedes\u2019 Palimpsest to 2000 \u2013 DVD. http:\/\/www.youtube.com\/watch?v=_rHv3OiaVC8&feature=related
– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick\u2019s formula)
http:\/\/jwilson.coe.uga.edu\/emt668\/EMT668.Folders.F97\/Nipper\/Pick’sTheorem.html
– Heather Bridges \u2013 Pick\u2019s and Euler\u2019s Theorems. http:\/\/jwilson.coe.uga.edu\/emt669\/student.folders\/bailey.heather\/essay%202\/picks.html<\/p>\n

Sig<\/h3>\n

– Laurent Bussard. R\u00e8gles du jeu de Sig de Mauritanie. http:\/\/bussard.pagesperso-orange.fr\/mauritanie\/sig\/
– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos). http:\/\/globaltimoto.com\/pages\/game_08_Seig.htm
– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001) http:\/\/www.boardgamestudies.info\/pdf\/aux\/BGS4Depaulis1.pdf
– Site culturel du Sahara (vid\u00e9os). http:\/\/www.sahara-culture.com\/fr\/Jeuxpopulaires\/Jeuxfeminins\/Sig\/tabid\/106\/Default.aspx<\/p>\n

Rithmomachia<\/h3>\n

– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche \u00dcberlieferungen der Rithmomachie (Board Game Studies 1999)
http:\/\/www.boardgamestudies.info\/pdf\/issue2\/BGS2Mebben.pdf
– Jos\u00e9 M. N\u00fa\u00f1ez Espallargas (Univ. Barcelona). La aritm\u00e9tica de Boecio y la ritmomaquia: teor\u00eda y pr\u00e1ctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004). http:\/\/estudiosmedievales.revistas.csic.es\/index.php\/estudiosmedievales\/article\/view\/187\/190
– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007). http:\/\/www.alexfedi.it\/medioevo\/risorse\/rithmo.html
– Boethius. De Institutione arithmetica (505).
http:\/\/daten.digitale-sammlungen.de\/~db\/0004\/bsb00047475\/images\/index.html?id=00047475&fip=109.237.48.125&no=8&seite=6
– Blog about Rithmomachia (Paesi Bassi, 2004) http:\/\/aritmomachia.blogspot.com\/
– J. F. Gilles. Rythmomachie, diverses r\u00e8gles du jeu. http:\/\/www.jf-gilles.eu\/<\/p>\n

Backgammon<\/h3>\n

– Dario De Toffoli, Il grande libro del Backgammon<\/i>, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4<\/a><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”1_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_1″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_2″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22″ background_color=”#8224e3″ global_colors_info=”{}”][et_pb_fullwidth_header title=”Ludyssea – Viaggio matematico tra i giochi antichi” subhead=”Mostra – laboratorio” content_max_width=”none” admin_label=”Fullwidth Header” _builder_version=”3.16″ background_color=”rgba(255, 255, 255, 0)” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”off” button_two_letter_spacing__hover_enabled=”off” button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.22″ global_colors_info=”{}”][et_pb_row column_structure=”3_4,1_4″ _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”3_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text admin_label=”Text” _builder_version=”3.27.4″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”]<\/p>\n

video Ludyssea\u00a0<\/a><\/h2>\n

Scarica il pdf di presentazione:\u00a0Ludyssea-MostraLaboratorioGiochiEMatematica<\/a><\/p>\n

“Considerate la vostra semenza: fatti non foste a viver come bruti, ma per giuocar li giuochi e farne scienza!”<\/p>\n

\"\"<\/a>Non diceva forse cos\u00ed l’Ulisse di Dante per spronare i suoi compagni di viaggio (e di gioco)? Nel suo peregrinare da una parte all’altra verso gli orizzonti Mediterranei, Ludysseus cercava di scoprire le radici profonde delle culture di quei popoli attraverso i loro giochi e la matematica ivi nascosta. Ludyssea \u00e8 un viaggio che vi porta dalla geometria dell\u2019Ostomachion Archimedeo (quadrato scomposto in 14 figure diverse) alle probabilit\u00e0 nascoste nelle varianti del Backgammon (Ludus Duodecim Scriptorum per i Romani, Tavli per Greci e Turchi); dalle configurazioni periodiche del Mancaley (gioco siriano della semina), alla legge binomiale del Sig Maghrebino, fino all’aritmetica medievale insegnata in Italia e in Francia attraverso la Rithmomachia, la “Battaglia dei Numeri” (una specie di scacchi con somme e prodotti). “E volta nostra poppa nel mattino, de’ remi facemmo ali al folle volo, sempre giuocando a scacchi e a nascondino\u201c<\/p>\n

A cura di Cesco Reale (Festival di Giochi Matematici<\/a>). In collaborazione con MateFitness<\/a> (CNR-PSC) e con CEMEA<\/a> Veneto. Con il patrocinio del Museo Svizzero del Gioco<\/a> e il supporto del Festival della Scienza<\/a>.<\/p>\n

MOSTRA E LABORATORIO<\/p>\n

I vari giochi presenti a Ludyssea vengono illustrati e fatti giocare spiegando il contesto storico-culturale in cui sono (o erano) giocati e le regole. In seguito si propone al pubblico di analizzare alcune situazioni di gioco che hanno legami con la matematica. L\u2019attivit\u00e0 \u00e8 pensata per scuole e festival, ma anche per un pubblico pi\u00f9 esigente, potendo essere fruita a vari livelli di difficolt\u00e0. Inoltre Ludyssea \u00e8 fruibile anche come mostra, attraverso la lettura dei pannelli e i giochi.<\/p>\n

Allestimenti passati:<\/p>\n

– Festival dellaScienza 2010, Genova <\/a><\/p>\n

–InfinitaMente<\/a> 2011,\u00a0 <\/a>Univ<\/a>. <\/a>Verona<\/a><\/p>\n

–\u00a0<\/a>SettimanadellaMatematica 2012, Univ. Brescia<\/a><\/p>\n

I GIOCHI:<\/p>\n

– Ostomachion: teorema di Pick; qual \u00e8 l’area delle figure seguenti? Cercate di riprodurle con i pezzi del gioco. In quanti modi si pu\u00f3 ricostruire il quadrato? Animazioni al computer.<\/p>\n

– Mancala: il resto della divisione. Quale mossa mi permette di minacciare una cattura? Gruppi di marcia e configurazioni periodiche. Etnomatematica: confronto tra le analisi strategiche di matematici ed esperti locali.<\/p>\n

– Sig: i dadi binari e la legge binomiale. Video di donne Saharawi che giocano nel deserto.<\/p>\n

– Rithmomachia: presentazione dell’Arithmetica di Boezio. Aritmetica, geometria e musica nella filosofia pitagorica. Successioni aritmetiche, geometriche e armoniche.<\/p>\n

– Backgammon: confronto con il Ludus Duodecim Scriptorum (antico gioco Romano) e con le versioni moderne in Grecia; in questa situazione qual \u00e8 la mossa migliore per minimizzare la probabilit\u00e0 che la pedina sia catturata?<\/p>\n

MATERIALI<\/p>\n

La mostra \u00e8 composta da 10 pannelli (A1- dimensioni 84 x 60 cm) e da 20 giochi in legno utilizzabili dal pubblico durante i laboratori o per partite libere. Spazio necessario: 50-100 mq.<\/p>\n

Sitobibliografia<\/strong><\/h1>\n

Mancala<\/h3>\n

– Marc Chemillier (Univ. Caen). El\u00e9ments pour une ethnomath\u00e9matique de l’aw\u00e9l\u00e9 (Mathematics and Social Sciences n. 181, 2008)<\/p>\n

– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)<\/p>\n

– Marino Carpignano (Progetto Abstrakta). http:\/\/www.pergioco.net\/Giochi\/GiochiDiTavoliere\/Mancala\/Mancala.htm<\/p>\n

– http:\/\/www.awale.info<\/p>\n

– Univ. Lisboa. Matem\u00e1tica em Jogo \u2014 exposi\u00e7\u00e3o virtual. http:\/\/mat.fc.ul.pt\/divulgacao\/mej\/expo_virtual<\/p>\n

Ostomachion<\/h3>\n

– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede. http:\/\/areeweb.polito.it\/didattica\/polymath\/htmlS\/probegio\/GAMEMATH\/Stomachion\/Stomachion.htm<\/p>\n

– Stomachion (Visualization of the 268 basic solutions) http:\/\/4umi.com\/play\/stomachion\/ Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion). http:\/\/www.math.ucsd.edu\/~fan\/stomach\/<\/p>\n

– The Walters Art Museum. The story of the Archimedes\u2019 Palimpsest to 2000 \u2013 DVD. http:\/\/www.youtube.com\/watch?v=_rHv3OiaVC8&feature=related<\/p>\n

– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick\u2019s formula) http:\/\/jwilson.coe.uga.edu\/emt668\/EMT668.Folders.F97\/Nipper\/Pick’sTheorem.html<\/p>\n

– Heather Bridges \u2013 Pick\u2019s and Euler\u2019s Theorems. http:\/\/jwilson.coe.uga.edu\/emt669\/student.folders\/bailey.heather\/essay%202\/picks.html<\/p>\n

Sig<\/h3>\n

– Laurent Bussard. R\u00e8gles du jeu de Sig de Mauritanie. http:\/\/bussard.pagesperso-orange.fr\/mauritanie\/sig\/<\/p>\n

– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos). http:\/\/globaltimoto.com\/pages\/game_08_Seig.htm<\/p>\n

– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001) http:\/\/www.boardgamestudies.info\/pdf\/aux\/BGS4Depaulis1.pdf<\/p>\n

– Site culturel du Sahara (vid\u00e9os). http:\/\/www.sahara-culture.com\/fr\/Jeuxpopulaires\/Jeuxfeminins\/Sig\/tabid\/106\/Default.aspx<\/p>\n

Rithmomachia<\/h3>\n

– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche \u00dcberlieferungen der Rithmomachie (Board Game Studies 1999) http:\/\/www.boardgamestudies.info\/pdf\/issue2\/BGS2Mebben.pdf<\/p>\n

– Jos\u00e9 M. N\u00fa\u00f1ez Espallargas (Univ. Barcelona). La aritm\u00e9tica de Boecio y la ritmomaquia: teor\u00eda y pr\u00e1ctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004). http:\/\/estudiosmedievales.revistas.csic.es\/index.php\/estudiosmedievales\/article\/view\/187\/190<\/p>\n

– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007). http:\/\/www.alexfedi.it\/medioevo\/risorse\/rithmo.html<\/p>\n

– Boethius. De Institutione arithmetica (505). http:\/\/daten.digitale-sammlungen.de\/~db\/0004\/bsb00047475\/images\/index.html?id=00047475&fip=109.237.48.125&no=8&seite=6<\/p>\n

– Blog about Rithmomachia (Paesi Bassi, 2004) http:\/\/aritmomachia.blogspot.com\/<\/p>\n

– J. F. Gilles. Rythmomachie, diverses r\u00e8gles du jeu. http:\/\/www.jf-gilles.eu\/<\/p>\n

Backgammon<\/h3>\n

– Dario De Toffoli, Il grande libro del Backgammon<\/i>, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4<\/a>
\n[\/et_pb_text][\/et_pb_column][et_pb_column type=”1_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_1″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_2″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22″ background_color=”#8224e3″ global_colors_info=”{}”][et_pb_fullwidth_header title=”Ludyss\u00e9e – Voyage math\u00e9matique \u00e0 travers les jeux anciens” subhead=”Expo – atelier” content_max_width=”none” admin_label=”Fullwidth Header” _builder_version=”3.16″ background_color=”rgba(255, 255, 255, 0)” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”off” button_two_letter_spacing__hover_enabled=”off” button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.22″ global_colors_info=”{}”][et_pb_row column_structure=”3_4,1_4″ _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”3_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text admin_label=”Text” _builder_version=”3.27.4″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”]<\/p>\n

vid\u00e9o Ludyss\u00e9e<\/a><\/h2>\n

PDF de pr\u00e9sentation: Ludyss\u00e9e-ExpoAtelierJeuxEtMaths<\/a><\/p>\n

“Consid\u00e9rez ici votre naissance:
\nvous n\u2019\u00eates pas n\u00e9s pour vivre comme des brutes,
\nmais pour jouer les jeux et en faire science!”<\/p>\n

\"\"<\/a><\/p>\n

N\u2019\u00e9tait-ce pas par ces mots que l\u2019Ulysse de Dante incitait ses compagnons de voyage (et de jeu) ? Dans ses p\u00e9r\u00e9grinations d’un c\u00f4t\u00e9 \u00e0 l\u2019autre de la M\u00e9diterran\u00e9e, Ludysseus essayait de d\u00e9couvrir \u00e0 travers leurs jeux les racines profondes des cultures de ces peuples et de trouver les math\u00e9matiques qui y sont cach\u00e9es. Ludyss\u00e9e est un voyage qui vous emm\u00e8ne de la g\u00e9om\u00e9trie de l’Ostomachion d\u2019Archim\u00e8de (un carr\u00e9 divis\u00e9 en 14 figures diff\u00e9rentes) aux probabilit\u00e9s cach\u00e9es dans les variantes du Backgammon (Ludus Duodecim Scriptorum pour les Romains, Tavli pour les Grecs et les Turcs). Il vous fait \u00e9galement voyager des configurations p\u00e9riodiques du Mancaley (jeu syrien des semailles) \u00e0 la loi binomiale du Sig Maghrebin, et vous am\u00e8ne \u00e0 d\u00e9courvrir l’arithm\u00e9tique m\u00e9di\u00e9vale enseign\u00e9e en Italie et en France \u00e0 travers la Rithmomachia, la \u00abbataille des nombres\u00bb (une sorte de jeu d’\u00e9checs avec des nombres).<\/p>\n

De Cesco Reale (Festival de Jeux Math\u00e9matiques). En collaboration avec MateFitness (CNR-PSC) et avec CEMEA Veneto. Avec le patronage du Mus\u00e9e Suisse du Jeu et le support du Festival de la Science.<\/p>\n

EXPOSITION\u00a0 ET ATELIER
\nLes diff\u00e9rents jeux de Ludyss\u00e9e sont illustr\u00e9s \u00e0 l\u2019aide de panneaux et peuvent \u00eatre exp\u00e9riment\u00e9s. Le contexte historique-culturel dans lequel ils \u00e9taient jou\u00e9s, ainsi que leurs r\u00e8gles sont expliqu\u00e9s. Une analyse math\u00e9matique des jeux est faite \u00e0 travers diff\u00e9rentes situations.
\nCes activit\u00e9s sont con\u00e7ues pour les \u00e9coles ou pour un festival. Elles peuvent satisfaire diff\u00e9rents publics, pr\u00e9sentant plusieurs niveaux de difficult\u00e9.<\/p>\n

Pr\u00e9sentations pr\u00e9c\u00e9dentes:
\n– Festival della Scienza 2010, Genova (IT)<\/a>
\n– InfinitaMente 2011, Univ. Verona (IT)<\/a>
\n– Settimana della Matematica 2012, Univ. Brescia (IT)<\/p>\n

JEUX:
\n– Ostomachion: calcul \u00e0 l\u2019aide du th\u00e9or\u00e8me de Pick de l\u2019aire des diff\u00e9rents pi\u00e8ces. Recherche des diff\u00e9rentes mani\u00e8res de reconstruire le puzzle d\u2019Archim\u00e8de. Animations \u00e0 l\u2019ordinateur pr\u00e9sentant cette recherche.
\n– Mancala: Recherche des mouvements permettant de capturer des graines. Groupes de marche et configurations p\u00e9riodiques. Ethno-math\u00e9matiques: comparaison entre les analyses strat\u00e9giques de math\u00e9maticiens et d’experts locaux.
\n– Sig: d\u00e9s binaires et loi binomiale. Vid\u00e9os de femmes sahraouies jouant au sig dans le d\u00e9sert.
\n– Rithmomachia: pr\u00e9sentation de l’Arithmetica de Bo\u00e8ce. Arithm\u00e9tique, g\u00e9om\u00e9trie et musique dans la philosophie pythagoricienne. S\u00e9quences arithm\u00e9tiques, g\u00e9om\u00e9triques et harmoniques.
\n– Backgammon: comparaison avec le Ludus Duodecim Scriptorum (ancien jeu Romain) et les versions modernes en Gr\u00e8ce; recherche dans une situation donn\u00e9e du coup permettant de minimiser la probabilit\u00e9 qu\u2019une pi\u00e8ce soit captur\u00e9e.
\nMAT\u00c9RIEL
\nL’exposition se compose de 10 panneaux (format A1, 84 x 60) et de 20 jeux en bois qui peuvent \u00eatre utilis\u00e9s par le public lors d\u2019ateliers ou de parties libres. Espace n\u00e9cessaire: 50-100 m2.<\/p>\n

Sitebibliographie<\/strong><\/h1>\n

Mancala<\/h3>\n

– Marc Chemillier (Univ. Caen). El\u00e9ments pour une ethnomath\u00e9matique de l’aw\u00e9l\u00e9 (Mathematics and Social Sciences n. 181, 2008)<\/p>\n

– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)<\/p>\n

– Marino Carpignano (Progetto Abstrakta). http:\/\/www.pergioco.net\/Giochi\/GiochiDiTavoliere\/Mancala\/Mancala.htm<\/p>\n

– http:\/\/www.awale.info<\/p>\n

– Univ. Lisboa. Matem\u00e1tica em Jogo \u2014 exposi\u00e7\u00e3o virtual. http:\/\/mat.fc.ul.pt\/divulgacao\/mej\/expo_virtual<\/p>\n

Ostomachion<\/h3>\n

– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede. http:\/\/areeweb.polito.it\/didattica\/polymath\/htmlS\/probegio\/GAMEMATH\/Stomachion\/Stomachion.htm<\/p>\n

– Stomachion (Visualization of the 268 basic solutions) http:\/\/4umi.com\/play\/stomachion\/ Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion). http:\/\/www.math.ucsd.edu\/~fan\/stomach\/<\/p>\n

– The Walters Art Museum. The story of the Archimedes\u2019 Palimpsest to 2000 \u2013 DVD. http:\/\/www.youtube.com\/watch?v=_rHv3OiaVC8&feature=related<\/p>\n

– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick\u2019s formula) http:\/\/jwilson.coe.uga.edu\/emt668\/EMT668.Folders.F97\/Nipper\/Pick’sTheorem.html<\/p>\n

– Heather Bridges \u2013 Pick\u2019s and Euler\u2019s Theorems. http:\/\/jwilson.coe.uga.edu\/emt669\/student.folders\/bailey.heather\/essay%202\/picks.html<\/p>\n

Sig<\/h3>\n

– Laurent Bussard. R\u00e8gles du jeu de Sig de Mauritanie. http:\/\/bussard.pagesperso-orange.fr\/mauritanie\/sig\/<\/p>\n

– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos). http:\/\/globaltimoto.com\/pages\/game_08_Seig.htm<\/p>\n

– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001) http:\/\/www.boardgamestudies.info\/pdf\/aux\/BGS4Depaulis1.pdf<\/p>\n

– Site culturel du Sahara (vid\u00e9os). http:\/\/www.sahara-culture.com\/fr\/Jeuxpopulaires\/Jeuxfeminins\/Sig\/tabid\/106\/Default.aspx<\/p>\n

Rithmomachia<\/h3>\n

– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche \u00dcberlieferungen der Rithmomachie (Board Game Studies 1999) http:\/\/www.boardgamestudies.info\/pdf\/issue2\/BGS2Mebben.pdf<\/p>\n

– Jos\u00e9 M. N\u00fa\u00f1ez Espallargas (Univ. Barcelona). La aritm\u00e9tica de Boecio y la ritmomaquia: teor\u00eda y pr\u00e1ctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004). http:\/\/estudiosmedievales.revistas.csic.es\/index.php\/estudiosmedievales\/article\/view\/187\/190<\/p>\n

– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007). http:\/\/www.alexfedi.it\/medioevo\/risorse\/rithmo.html<\/p>\n

– Boethius. De Institutione arithmetica (505). http:\/\/daten.digitale-sammlungen.de\/~db\/0004\/bsb00047475\/images\/index.html?id=00047475&fip=109.237.48.125&no=8&seite=6<\/p>\n

– Blog about Rithmomachia (Paesi Bassi, 2004) http:\/\/aritmomachia.blogspot.com\/<\/p>\n

– J. F. Gilles. Rythmomachie, diverses r\u00e8gles du jeu. http:\/\/www.jf-gilles.eu\/<\/p>\n

Backgammon<\/h3>\n

– Dario De Toffoli, Il grande libro del Backgammon<\/i>, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4<\/a>
\n[\/et_pb_text][\/et_pb_column][et_pb_column type=”1_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_1″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_2″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22″ background_color=”#8224e3″ global_colors_info=”{}”][et_pb_fullwidth_header title=”Ludyssea – Viaggio matematico tra i giochi antichi” subhead=”Mostra – laboratorio” content_max_width=”none” admin_label=”Fullwidth Header” _builder_version=”3.16″ background_color=”rgba(255, 255, 255, 0)” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”off” button_two_letter_spacing__hover_enabled=”off” button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.22″ global_colors_info=”{}”][et_pb_row column_structure=”3_4,1_4″ _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”3_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text admin_label=”Text” _builder_version=”3.27.4″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”]<\/p>\n

video Ludyssea\u00a0<\/a><\/h2>\n

Scarica il pdf di presentazione:\u00a0Ludyssea-MostraLaboratorioGiochiEMatematica<\/a><\/p>\n

“Considerate la vostra semenza: fatti non foste a viver come bruti, ma per giuocar li giuochi e farne scienza!”<\/p>\n

\"\"<\/a>Non diceva forse cos\u00ed l’Ulisse di Dante per spronare i suoi compagni di viaggio (e di gioco)? Nel suo peregrinare da una parte all’altra verso gli orizzonti Mediterranei, Ludysseus cercava di scoprire le radici profonde delle culture di quei popoli attraverso i loro giochi e la matematica ivi nascosta. Ludyssea \u00e8 un viaggio che vi porta dalla geometria dell\u2019Ostomachion Archimedeo (quadrato scomposto in 14 figure diverse) alle probabilit\u00e0 nascoste nelle varianti del Backgammon (Ludus Duodecim Scriptorum per i Romani, Tavli per Greci e Turchi); dalle configurazioni periodiche del Mancaley (gioco siriano della semina), alla legge binomiale del Sig Maghrebino, fino all’aritmetica medievale insegnata in Italia e in Francia attraverso la Rithmomachia, la “Battaglia dei Numeri” (una specie di scacchi con somme e prodotti). “E volta nostra poppa nel mattino, de’ remi facemmo ali al folle volo, sempre giuocando a scacchi e a nascondino\u201c<\/p>\n

A cura di Cesco Reale (Festival di Giochi Matematici<\/a>). In collaborazione con MateFitness<\/a> (CNR-PSC) e con CEMEA<\/a> Veneto. Con il patrocinio del Museo Svizzero del Gioco<\/a> e il supporto del Festival della Scienza<\/a>.<\/p>\n

MOSTRA E LABORATORIO<\/p>\n

I vari giochi presenti a Ludyssea vengono illustrati e fatti giocare spiegando il contesto storico-culturale in cui sono (o erano) giocati e le regole. In seguito si propone al pubblico di analizzare alcune situazioni di gioco che hanno legami con la matematica. L\u2019attivit\u00e0 \u00e8 pensata per scuole e festival, ma anche per un pubblico pi\u00f9 esigente, potendo essere fruita a vari livelli di difficolt\u00e0. Inoltre Ludyssea \u00e8 fruibile anche come mostra, attraverso la lettura dei pannelli e i giochi.<\/p>\n

Allestimenti passati:<\/p>\n

– Festival <\/a>della<\/a>Scienza<\/a> 2010, Genova <\/a><\/p>\n

–InfinitaMente<\/a> 2011,\u00a0 <\/a>Univ<\/a>. <\/a>Verona<\/a><\/p>\n

–\u00a0<\/a>Settimana<\/a>della<\/a>Matematica<\/a> 2012, <\/a>Univ<\/a>. Brescia<\/a><\/p>\n

I GIOCHI:<\/p>\n

– Ostomachion: teorema di Pick; qual \u00e8 l’area delle figure seguenti? Cercate di riprodurle con i pezzi del gioco. In quanti modi si pu\u00f3 ricostruire il quadrato? Animazioni al computer.<\/p>\n

– Mancala: il resto della divisione. Quale mossa mi permette di minacciare una cattura? Gruppi di marcia e configurazioni periodiche. Etnomatematica: confronto tra le analisi strategiche di matematici ed esperti locali.<\/p>\n

– Sig: i dadi binari e la legge binomiale. Video di donne Saharawi che giocano nel deserto.<\/p>\n

– Rithmomachia: presentazione dell’Arithmetica di Boezio. Aritmetica, geometria e musica nella filosofia pitagorica. Successioni aritmetiche, geometriche e armoniche.<\/p>\n

– Backgammon: confronto con il Ludus Duodecim Scriptorum (antico gioco Romano) e con le versioni moderne in Grecia; in questa situazione qual \u00e8 la mossa migliore per minimizzare la probabilit\u00e0 che la pedina sia catturata?<\/p>\n

MATERIALI<\/p>\n

La mostra \u00e8 composta da 10 pannelli (A1- dimensioni 84 x 60 cm) e da 20 giochi in legno utilizzabili dal pubblico durante i laboratori o per partite libere. Spazio necessario: 50-100 mq.<\/p>\n

Sitobibliografia<\/strong><\/h1>\n

Mancala<\/h3>\n

– Marc Chemillier (Univ. Caen). El\u00e9ments pour une ethnomath\u00e9matique de l’aw\u00e9l\u00e9 (Mathematics and Social Sciences n. 181, 2008)<\/p>\n

– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)<\/p>\n

– Marino Carpignano (Progetto Abstrakta). http:\/\/www.pergioco.net\/Giochi\/GiochiDiTavoliere\/Mancala\/Mancala.htm<\/p>\n

– http:\/\/www.awale.info<\/p>\n

– Univ. Lisboa. Matem\u00e1tica em Jogo \u2014 exposi\u00e7\u00e3o virtual. http:\/\/mat.fc.ul.pt\/divulgacao\/mej\/expo_virtual<\/p>\n

Ostomachion<\/h3>\n

– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede. http:\/\/areeweb.polito.it\/didattica\/polymath\/htmlS\/probegio\/GAMEMATH\/Stomachion\/Stomachion.htm<\/p>\n

– Stomachion (Visualization of the 268 basic solutions) http:\/\/4umi.com\/play\/stomachion\/ Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion). http:\/\/www.math.ucsd.edu\/~fan\/stomach\/<\/p>\n

– The Walters Art Museum. The story of the Archimedes\u2019 Palimpsest to 2000 \u2013 DVD. http:\/\/www.youtube.com\/watch?v=_rHv3OiaVC8&feature=related<\/p>\n

– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick\u2019s formula) http:\/\/jwilson.coe.uga.edu\/emt668\/EMT668.Folders.F97\/Nipper\/Pick’sTheorem.html<\/p>\n

– Heather Bridges \u2013 Pick\u2019s and Euler\u2019s Theorems. http:\/\/jwilson.coe.uga.edu\/emt669\/student.folders\/bailey.heather\/essay%202\/picks.html<\/p>\n

Sig<\/h3>\n

– Laurent Bussard. R\u00e8gles du jeu de Sig de Mauritanie. http:\/\/bussard.pagesperso-orange.fr\/mauritanie\/sig\/<\/p>\n

– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos). http:\/\/globaltimoto.com\/pages\/game_08_Seig.htm<\/p>\n

– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001) http:\/\/www.boardgamestudies.info\/pdf\/aux\/BGS4Depaulis1.pdf<\/p>\n

– Site culturel du Sahara (vid\u00e9os). http:\/\/www.sahara-culture.com\/fr\/Jeuxpopulaires\/Jeuxfeminins\/Sig\/tabid\/106\/Default.aspx<\/p>\n

Rithmomachia<\/h3>\n

– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche \u00dcberlieferungen der Rithmomachie (Board Game Studies 1999) http:\/\/www.boardgamestudies.info\/pdf\/issue2\/BGS2Mebben.pdf<\/p>\n

– Jos\u00e9 M. N\u00fa\u00f1ez Espallargas (Univ. Barcelona). La aritm\u00e9tica de Boecio y la ritmomaquia: teor\u00eda y pr\u00e1ctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004). http:\/\/estudiosmedievales.revistas.csic.es\/index.php\/estudiosmedievales\/article\/view\/187\/190<\/p>\n

– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007). http:\/\/www.alexfedi.it\/medioevo\/risorse\/rithmo.html<\/p>\n

– Boethius. De Institutione arithmetica (505). http:\/\/daten.digitale-sammlungen.de\/~db\/0004\/bsb00047475\/images\/index.html?id=00047475&fip=109.237.48.125&no=8&seite=6<\/p>\n

– Blog about Rithmomachia (Paesi Bassi, 2004) http:\/\/aritmomachia.blogspot.com\/<\/p>\n

– J. F. Gilles. Rythmomachie, diverses r\u00e8gles du jeu. http:\/\/www.jf-gilles.eu\/<\/p>\n

Backgammon<\/h3>\n

– Dario De Toffoli, Il grande libro del Backgammon<\/i>, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4<\/a>
\n[\/et_pb_text][\/et_pb_column][et_pb_column type=”1_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_1″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][et_pb_sidebar orientation=”right” area=”et_pb_widget_area_2″ admin_label=”Sidebar” _builder_version=”3.0.74″ global_colors_info=”{}”][\/et_pb_sidebar][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22″ background_color=”#8224e3″ global_colors_info=”{}”][et_pb_fullwidth_header title=”Ludyssea – Viaggio matematico tra i giochi antichi” subhead=”Mostra – laboratorio” content_max_width=”none” admin_label=”Fullwidth Header” _builder_version=”3.16″ background_color=”rgba(255, 255, 255, 0)” global_colors_info=”{}” button_one_text_size__hover_enabled=”off” button_two_text_size__hover_enabled=”off” button_one_text_color__hover_enabled=”off” button_two_text_color__hover_enabled=”off” button_one_border_width__hover_enabled=”off” button_two_border_width__hover_enabled=”off” button_one_border_color__hover_enabled=”off” button_two_border_color__hover_enabled=”off” button_one_border_radius__hover_enabled=”off” button_two_border_radius__hover_enabled=”off” button_one_letter_spacing__hover_enabled=”off” button_two_letter_spacing__hover_enabled=”off” button_one_bg_color__hover_enabled=”off” button_two_bg_color__hover_enabled=”off”][\/et_pb_fullwidth_header][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.22″ global_colors_info=”{}”][et_pb_row column_structure=”3_4,1_4″ _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”3_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text admin_label=”Text” _builder_version=”3.27.4″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”]<\/p>\n

video Ludyssea\u00a0<\/a><\/h2>\n

Scarica il pdf di presentazione:\u00a0Ludyssea-MostraLaboratorioGiochiEMatematica<\/a><\/p>\n

“Considerate la vostra semenza: fatti non foste a viver come bruti, ma per giuocar li giuochi e farne scienza!”<\/p>\n

\"\"<\/a>Non diceva forse cos\u00ed l’Ulisse di Dante per spronare i suoi compagni di viaggio (e di gioco)? Nel suo peregrinare da una parte all’altra verso gli orizzonti Mediterranei, Ludysseus cercava di scoprire le radici profonde delle culture di quei popoli attraverso i loro giochi e la matematica ivi nascosta. Ludyssea \u00e8 un viaggio che vi porta dalla geometria dell\u2019Ostomachion Archimedeo (quadrato scomposto in 14 figure diverse) alle probabilit\u00e0 nascoste nelle varianti del Backgammon (Ludus Duodecim Scriptorum per i Romani, Tavli per Greci e Turchi); dalle configurazioni periodiche del Mancaley (gioco siriano della semina), alla legge binomiale del Sig Maghrebino, fino all’aritmetica medievale insegnata in Italia e in Francia attraverso la Rithmomachia, la “Battaglia dei Numeri” (una specie di scacchi con somme e prodotti). “E volta nostra poppa nel mattino, de’ remi facemmo ali al folle volo, sempre giuocando a scacchi e a nascondino\u201c<\/p>\n

A cura di Cesco Reale (Festival di Giochi Matematici<\/a>). In collaborazione con MateFitness<\/a> (CNR-PSC) e con CEMEA<\/a> Veneto. Con il patrocinio del Museo Svizzero del Gioco<\/a> e il supporto del Festival della Scienza<\/a>.<\/p>\n

MOSTRA E LABORATORIO<\/p>\n

I vari giochi presenti a Ludyssea vengono illustrati e fatti giocare spiegando il contesto storico-culturale in cui sono (o erano) giocati e le regole. In seguito si propone al pubblico di analizzare alcune situazioni di gioco che hanno legami con la matematica. L\u2019attivit\u00e0 \u00e8 pensata per scuole e festival, ma anche per un pubblico pi\u00f9 esigente, potendo essere fruita a vari livelli di difficolt\u00e0. Inoltre Ludyssea \u00e8 fruibile anche come mostra, attraverso la lettura dei pannelli e i giochi.<\/p>\n

Allestimenti passati:<\/p>\n

– Festival <\/a>della<\/a>Scienza<\/a> 2010, Genova <\/a><\/p>\n

–InfinitaMente<\/a> 2011,\u00a0 <\/a>Univ<\/a>. <\/a>Verona<\/a><\/p>\n

–\u00a0<\/a>Settimana<\/a>della<\/a>Matematica<\/a> 2012, <\/a>Univ<\/a>. Brescia<\/a><\/p>\n

I GIOCHI:<\/p>\n

– Ostomachion: teorema di Pick; qual \u00e8 l’area delle figure seguenti? Cercate di riprodurle con i pezzi del gioco. In quanti modi si pu\u00f3 ricostruire il quadrato? Animazioni al computer.<\/p>\n

– Mancala: il resto della divisione. Quale mossa mi permette di minacciare una cattura? Gruppi di marcia e configurazioni periodiche. Etnomatematica: confronto tra le analisi strategiche di matematici ed esperti locali.<\/p>\n

– Sig: i dadi binari e la legge binomiale. Video di donne Saharawi che giocano nel deserto.<\/p>\n

– Rithmomachia: presentazione dell’Arithmetica di Boezio. Aritmetica, geometria e musica nella filosofia pitagorica. Successioni aritmetiche, geometriche e armoniche.<\/p>\n

– Backgammon: confronto con il Ludus Duodecim Scriptorum (antico gioco Romano) e con le versioni moderne in Grecia; in questa situazione qual \u00e8 la mossa migliore per minimizzare la probabilit\u00e0 che la pedina sia catturata?<\/p>\n

MATERIALI<\/p>\n

La mostra \u00e8 composta da 10 pannelli (A1- dimensioni 84 x 60 cm) e da 20 giochi in legno utilizzabili dal pubblico durante i laboratori o per partite libere. Spazio necessario: 50-100 mq.<\/p>\n

Sitobibliografia<\/strong><\/h1>\n

Mancala<\/h3>\n

– Marc Chemillier (Univ. Caen). El\u00e9ments pour une ethnomath\u00e9matique de l’aw\u00e9l\u00e9 (Mathematics and Social Sciences n. 181, 2008)<\/p>\n

– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)<\/p>\n

– Marino Carpignano (Progetto Abstrakta). http:\/\/www.pergioco.net\/Giochi\/GiochiDiTavoliere\/Mancala\/Mancala.htm<\/p>\n

– http:\/\/www.awale.info<\/p>\n

– Univ. Lisboa. Matem\u00e1tica em Jogo \u2014 exposi\u00e7\u00e3o virtual. http:\/\/mat.fc.ul.pt\/divulgacao\/mej\/expo_virtual<\/p>\n

Ostomachion<\/h3>\n

– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede. http:\/\/areeweb.polito.it\/didattica\/polymath\/htmlS\/probegio\/GAMEMATH\/Stomachion\/Stomachion.htm<\/p>\n

– Stomachion (Visualization of the 268 basic solutions) http:\/\/4umi.com\/play\/stomachion\/ Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion). http:\/\/www.math.ucsd.edu\/~fan\/stomach\/<\/p>\n

– The Walters Art Museum. The story of the Archimedes\u2019 Palimpsest to 2000 \u2013 DVD. http:\/\/www.youtube.com\/watch?v=_rHv3OiaVC8&feature=related<\/p>\n

– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick\u2019s formula) http:\/\/jwilson.coe.uga.edu\/emt668\/EMT668.Folders.F97\/Nipper\/Pick’sTheorem.html<\/p>\n

– Heather Bridges \u2013 Pick\u2019s and Euler\u2019s Theorems. http:\/\/jwilson.coe.uga.edu\/emt669\/student.folders\/bailey.heather\/essay%202\/picks.html<\/p>\n

Sig<\/h3>\n

– Laurent Bussard. R\u00e8gles du jeu de Sig de Mauritanie. http:\/\/bussard.pagesperso-orange.fr\/mauritanie\/sig\/<\/p>\n

– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos). http:\/\/globaltimoto.com\/pages\/game_08_Seig.htm<\/p>\n

– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001) http:\/\/www.boardgamestudies.info\/pdf\/aux\/BGS4Depaulis1.pdf<\/p>\n

– Site culturel du Sahara (vid\u00e9os). http:\/\/www.sahara-culture.com\/fr\/Jeuxpopulaires\/Jeuxfeminins\/Sig\/tabid\/106\/Default.aspx<\/p>\n

Rithmomachia<\/h3>\n

– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche \u00dcberlieferungen der Rithmomachie (Board Game Studies 1999) http:\/\/www.boardgamestudies.info\/pdf\/issue2\/BGS2Mebben.pdf<\/p>\n

– Jos\u00e9 M. N\u00fa\u00f1ez Espallargas (Univ. Barcelona). La aritm\u00e9tica de Boecio y la ritmomaquia: teor\u00eda y pr\u00e1ctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004). http:\/\/estudiosmedievales.revistas.csic.es\/index.php\/estudiosmedievales\/article\/view\/187\/190<\/p>\n

– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007). http:\/\/www.alexfedi.it\/medioevo\/risorse\/rithmo.html<\/p>\n

– Boethius. De Institutione arithmetica (505). http:\/\/daten.digitale-sammlungen.de\/~db\/0004\/bsb00047475\/images\/index.html?id=00047475&fip=109.237.48.125&no=8&seite=6<\/p>\n

– Blog about Rithmomachia (Paesi Bassi, 2004) http:\/\/aritmomachia.blogspot.com\/<\/p>\n

– J. F. Gilles. Rythmomachie, diverses r\u00e8gles du jeu. http:\/\/www.jf-gilles.eu\/<\/p>\n

Backgammon<\/h3>\n

– Dario De Toffoli, Il grande libro del Backgammon<\/i>, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4<\/a>
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