Download e-book for iPad: A History of Chinese Mathematics by Jean-Claude Martzloff

By Jean-Claude Martzloff

ISBN-10: 3540337822

ISBN-13: 9783540337829

This e-book is made of elements, the 1st dedicated to basic, historic and cultural history, and the second one to the improvement of every subdiscipline that jointly contain chinese language arithmetic. The publication is uniquely obtainable, either as a topical reference paintings, and in addition as an summary that may be learn and reread at many degrees of class through either sinologists and mathematicians alike.

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This ebook is made from elements, the 1st dedicated to basic, historic and cultural heritage, and the second one to the advance of every subdiscipline that jointly contain chinese language arithmetic. The ebook is uniquely available, either as a topical reference paintings, and likewise as an outline that may be learn and reread at many degrees of class by way of either sinologists and mathematicians alike.

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2), Hero's formula for the area of a triangle and summary data about polyhedra (Fig. 3), conic sections (Fig. 4), and the stereometry of regular polyhedra. It also contains a complete treatise of sphcrical trigonometry. ir (Fig. 5), the accuracy of which leaves nothing to be desired (Fig. 5):51 4%ernard-Maitre ( 5 ) , 1942, p. 16. 47This work was subsequently renamed the Xznfa suanshu or Xznfa lishu (Treatise of Mathematics (resp. e. according to the European methods)). Here "mathematics" suan and "mathematical astronomy" li are synonymous.

211. , pp. 148-151 (list obtained by perusing: Songshi, "Yiwenzhi;" Chongwen zongmu; Suanfa tongzong; Suichu tang shumu; Yang Hui suanfa; Xin yzxiang ,fayao; Zhizhai shulu jieti; preface of the Siyuan yujian compiled by Zu Yi). ''Cf. Li Qun ( l ' ) , 1975, p. 101 ff. In modern notation, Shen Gua's summation formula corresponds to + where a and b are given integers and A = a (n - l ) , B = b + ( n - l ) , respectively. More precisely, Shen Gua was interested in calculating the number of objects composing a solid made of n superposed rectangular layers having ( a k ) ( b k ) objects each (0 5 k 5 n - 1 ) respectively, each dimension being diminished by one unit from each layer to the next.

75According to the theory of the "Canopy of Heaven" (gaitian) described by the Zhoubi suanjing, the universe is finite. On the other hand, according to the theory of "the announcement of the night" (translation of xuanye by Ho Peng-Yoke ( l ) , 1966, p. ' difficult t o accept and apparently futile. " (qie lifenzhongmoxian dun you qiuzuo81 zhi ,fa er rno ihi sue But the criticism of geometry was not limited to the question of the strange ordering of the theorems. 84 is infinite. It is known that infinitist conceptions also existed in ancient Greece.

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