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Paulus GERDES & Ahmed DJEBBAR LES MATHEMATIQUES DANS L'HISTOIRE ET LES CULTURES AFRICAINES Une bibliographie annotée Union Mathématique Africaine 2004 Edition française : Unions Mathématique Africaine Commission Africaine d’Histoire des Mathématiques (AMUCHMA) U.F.R. de Mathématiques, Université des Sciences et des Technologies de Lille, 2007. Editions anglaises : Première édition : Africain Mathematical Union, Cape Town, Afrique du Sud, 2004. Seconde édition : Lulu Editeur, 2007. Les auteurs : Paulus GERDES Research Centre for Mathematics, Culture and Education, C.P. 915, Maputo, Mozambique. Tel. : +258 1 49 45 04 E-mail : [email protected] Ahmed DJEBBAR U.F.R. de Mathématiques, Bt. M2 Université des Sciences et des Technologies de Lille 59655 Villeneuve d’Asq Cedex, France Tel. : + 33 1 45 33 74 65 E-mail : [email protected] [email protected] 2 Table des matières PAGES Préface du Président de l'Union Mathématique Africaine (Pr. 5 Jan Persens) Présentation 6 Bibliographie A 9 B 30 C 49 D 58 E 77 F 87 G 92 H 123 I 131 J 136 K 139 L 149 M 160 N 172 O 175 P 180 R 186 S 196 T 214 U 221 V 223 W 228 Y 235 Z 237 Appendices 1 Sur des mathématiciens d'origine africaine/de la Diaspora 245 2 Publications d'auteurs africains sur l'histoire des mathématiques 250 en dehors de l'Afrique (incluant les comptes-rendus de ces publications) 3 PAGES 3 Sur le calcul du temps et l'astronomie dans l'histoire et les 253 cultures africaines 4 Les jeux de ficelle en Afrique 271 5 Exemples de livres et de livrets publiés par des mathématiciens 276 africains 6 Jeux de quadrillages en Afrique 286 7 Quelques mathématiciens africains pionniers du XXe siècle 298 8 Note sur les recherches inspirées par la reconstruction 300 historique des idées mathématiques contenues dans la tradition géométrique des Sona du centre de l'Afrique Australe Index 1 Index thématique 304 2 Index des pays et des régions 310 3 Index des auteurs 316 4 Index ethnographique et linguistique 328 5 Index des revues 330 6 Index des mathématiciens 339 Membres de la Commission de l'Union Mathématique Africaine sur 341 l'Histoire des Mathématiques en Afrique (AMUCHMA) 4 Préface On ne peut que faire bon accueil à cette très importante bibliographie annotée sur les mathématiques dans l'histoire et les cultures africaines. Nous sommes déjà au début du troisième millénaire et, pourtant, nous sommes souvent frappés par des attitudes, en grande partie basées sur l'ignorance, au sujet des contributions mathématiques de l'Afrique et des Africains. Je suis sûr que c'est ce phénomène ainsi que l'expérience et la connaissance collectives de Gerdes et de Djebbar qui les ont amené à concevoir cette publication. C'est évidemment une lourde tâche. Cette publication nous informe sur l'histoire des mathématiques en Afrique et sur les mathématiques dans l'histoire de l'Afrique. Il était également approprié d'inclure, comme ils l'ont fait, les contributions des Africains vivant hors de l'Afrique, ou comme on le dit généralement, la Diaspora africaine. Car, souvent, la participation et l'impact des Africains dans la vie et le développement hors de l'Afrique, particulièrement dans les pays développés sont, consciemment ou inconsciemment, sous- estimés ou même ignorés. Les mathématiques dans l'histoire et les cultures africaines: une bibliographie annotée, est assuré d'avoir un impact majeur sur les programmes des cours de (l'histoire des) mathématiques en Afrique. Le rôle des mathématiciens africains dans l'astronomie, le calcul du temps et les calendriers peuvent maintenant être recherchés et appréciés plus complètement. En incluant les mathématiques dans les cultures africaines, les auteurs ont attaché une valeur significative à la nature systématique, analytique et structurée des cultures africaines. Ainsi, les jeux de ficelles et les jeux de quadrillage apparaissent comme des activités mathématiques significatives tout en étant des formes de relaxation. A notre connaissance cette bibliographie, de plus de mille références, n'est pas seulement la plus complète jamais réalisée, mais elle couvre également le continent africain dans sa totalité et à travers de nombreux siècles tout en identifiant "les liens historiques à travers la Méditerranée et les océans". Ce dernier aspect est important parce qu'il met en perspective les résultats des mathématiques dites occidentales. Je crois qu'il y a une nécessité pour les étudiants et les chercheurs africains, particulièrement ceux de la nouvelle génération, à se rendre compte que les Africains ont apporté des contributions significatives à la science et aux mathématiques. Cette réalisation devrait leur servir d'inspiration. Le développement économique et technologique de l'Afrique à l'époque moderne dépend des diverses applications des sciences mathématiques. S'intéresser à ce qui a été produit par les ancêtres, est potentiellement important pour les générations du nouveau savoir, en particulier à l'aire des économies basées sur la connaissance. Au nom de l'Union Mathématique Africaine, je tiens à remercier sincèrement les Professeurs Paulus Gerdes et Ahmed Djebbar pour leur contribution. Ils sont, en effet, deux fidèles dans notre quête pour exhumer et mettre en lumière les contributions des Africains dans la recherche et l'enseignement mathématiques. Jan Persens, Ph.D Président de l'Union Mathématique Africaine Bellville, Afrique du Sud Juin 2004 5 Présentation Une des premières mesures prises par le Comité Exécutif de l'Union Mathématique Africaine (U.M.A.), élu au 2e Congrès Panafricain des Mathématiciens (avril 1986, Jos, Nigéria), sous la présidence du Professeur Aderemi Kuku, a été de créer une Commission de l’U.M.A. sur l'histoire des mathématiques en Afrique (AMUCHMA). Les deux auteurs ont été nommés, respectivement Président et Secrétaire. Aux congrès suivants, en 1991 (Nairobi, Kenya), en 1995 (Ifrane, Maroc) et en 2000 (Le Cap, Afrique du Sud), les auteurs ont été réélus. Comme coordonnateurs de la commission, nous avons tenté de stimuler la recherche, de collecter et diffuser le plus d’informations possibles concernant l'histoire des mathématiques en Afrique. Grâce aux nombreux travaux présentés dans des colloques et des séminaires organisés durant ces années, nous avons édité pas moins de 29 numéros du Bulletin de l’AMUCHMA. Nous voudrions présenter aux délégués du 6e Congrès Panafricain des Mathématiciens (septembre 2004, Tunis, Tunisie) la bibliographie suivante sur les mathématiques dans l'histoire et les cultures africaines. La bibliographie contient plus de mille références. C'est le résultat des informations que nous avons collectées à la fois dans le cadre de l'AMUCHMA et dans celui de notre propre recherche. Le premier auteur a également exploité les informations qu'il a recueillies, en tant que Secrétaire (1991-1995) de l'Association des Sciences Mathématiques de l'Afrique Australe (SAMSA), pour le Who's Who des mathématiques et de l'enseignement des mathématiques en Afrique australe (5-GER-92, 93, 95). Notre bibliographie tente d’englober le continent africain dans son ensemble, des temps les plus reculés jusqu’à aujourd’hui, sans oublier les liens historiques entre la Méditerranée et les Océans. Par exemple, plusieurs références insérées dans la bibliographie mettent en lumière la circulation des mathématiciens et des idées mathématiques entre le Maghreb (Nord Ouest de l’Afrique) et l’Andalus (Péninsule ibérique) durant le moyen âge. La présente bibliographie a été conçue pour, dans la mesure du possible, couvrir, compléter et mettre à jour les données. Des bibliographies partielles sur l'Afrique subsaharienne et le Maghreb ont été éditées antérieurement dans le bulletin de l'AMUCHMA (GER-92b, 92d ; DJE-9a, 95b), dans la revue internationale Historia Mathematica (GER-94f) et dans la revue espagnole d'histoire des sciences et de la technologie, LLULL (GER-04e). Organisation de la bibliographie Les références bibliographiques se rapportant directement à des idées mathématiques dans l'histoire et dans les cultures africaines sont incluses dans le corps principal de la bibliographie. Plusieurs annexes présentent des bibliographies complémentaires sur des thèmes liés au thème principal. Par exemple, comme plusieurs entrées dans le corps principal se rapportent à des mathématiciens d'origine africaine, l'annexe 1 présente une information bibliographique additionnelle sur des mathématiciens de la diaspora. Comme, au cours de l'histoire, des mathématiciens africains se sont souvent occupés d'astronomie, l'annexe 3 6 présente une bibliographie additionnelle sur le calcul du temps, les calendriers et l'astronomie dans les cultures africaines. Comme plusieurs auteurs ont discuté de l'utilisation des jeux de ficelles dans l'enseignement des mathématiques, l'annexe 4 présente une bibliographie additionnelle sur les jeux de ficelles en Afrique. Comme différentes études référencées dans le corps principal analysent les idées mathématiques des joueurs des jeux de quadrillage africains, l'annexe 6 présente une bibliographie additionnelle sur les jeux de quadrillage en Afrique. Pour compléter le panorama des recherches faites par des chercheurs africains dans le domaine de l'histoire des mathématiques, l'annexe 2 énumère les publications sur l'histoire des mathématiques faites par des chercheurs africains qui vivent hors d'Afrique. Cette recherche peut être liée, par exemple, aux mathématiques dans les cultures islamiques ou arabes ou à l'application des méthodologies de recherches développées en Afrique à d'autres contextes
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