Categories analogues d’accumulations discretes

by Li Shanlan, translated with commentary by Andrea Breard

Extent: 500 pages

Publisher: Les Belles Lettres

Subjects: Asian/Pacific Studies & Religions, Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Bibliotheque chinoise

Language: Chinese

Paperback (Published)

(November 2023)

ISBN: 9782251454917

4.88 x 7.44 inches

Price: $74.00

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Synopsis
Contributing Authors

Combien de futs de vin peut-on empiler pour former une pyramide tronquee dont les dimensions sont donnees ? Comment representer la suite de nombres impairs 1, 3, 5, 7, en lien avec leurs sommes partielles 1, 4, 9, 16, ? Pour repondre a de telles questions, a partir du XIe siecle, une veritable discipline mathematique, connue sous le nom d'” accumulations discretes “, se forma en Chine. Elle se nourrit d’abord de la geometrie et de l’algebre avant de prendre une tournure proprement arithmetique et independante des neuf themes etablis dans le canon des mathematiques chinoises depuis le premier siecle. L’auteur des Categories analogues d’accumulations discretes (1867), Li Shanlan, se prevaut d’etre le premier a avoir theorise le domaine. Mais quelle forme pourrait prendre une theorie mathematique en l’absence de tout discours demonstratif ? La lecture des Categories analogues montre en effet que l’organisation des ensembles d’objets mathematiques traites en quatre livres suit une logique strictement deductive combinee a une argumentation, tout aussi strictement, inductive. C’est sur la base d’une serie de triangles arithmetiques, en commencant par celui connu en Occident sous le nom de Triangle de Pascal (deja present en Chine depuis au moins le XIIe siecle), que Li Shanlan etablit un grand nombre de ” formules “, dont la fameuse identite combinatoire qui porte son nom. Font partie de sa boite a outils le langage naturel avant tout, les tableaux de baguettes a calcul, des diagrammes representant les suites des nombres et, implicitement, sa familiarite avec les Elements d’Euclide.

By (author) Li Shanlan
Translated with commentary by Andrea Breard

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