By Yvonne Dold-Samplonius, Benno van (Ed) Dalen
Die Frage nach der Ubermittlung mathematischen Wissens zwischen verschiedenen Kulturen ist in den letzten Jahren zu einem Schwerpunkt mathematikhistorischer Untersuchungen geworden. Hierzu ist die Zusammenarbeit von Spezialisten erforderlich, die sich mit verschiedenen Kulturen, Sprachen und mathematischen Traditionen beschaftigen. Das vorliegende Buch, das Ergebnis von Tagungen im Mathematischen Forschungsinstitut Oberwolfach und im learn and convention heart der Rockefeller starting place in Bellagio, behandelt die vielfaltigen Wege, die bei der Vermittlung mathematischen Wissens von den Babyloniern bis zum 17. Jahrhundert eingeschlagen wurden, und insbesondere den Austausch mathematischer Ideen von Indien uber China und die arabische Welt bis nach Westeuropa. Contents: okay. Vogel: A Surveying challenge Travels from China to Paris - J. Hoyrup: Seleucid options within the Babylonian oAlgebraico culture and their family members overseas - J. L. Berggren: a few historic and Medieval Approximations to Irrational Numbers and Their Transmission - J. Sesiano: A Reconstruction of Greek Multiplication Tables for Integers - A. Breard: difficulties of Pursuit: leisure arithmetic or Astronomy? - okay. Chemla / A. Keller: The Sanskrit karanis and the chinese language mian - S. R. Sarma: Rule of 3 and its diversifications in India - L. Dun: A Homecoming Stranger: Transmission of the tactic of Double fake place and the tale of Hiero's Crown - ok. Plofker: Use and Transmission of Iterative Approximations in India and the Islamic international - J. P. Hogendijk: Anthyphairetic Ratio concept in Medieval Islamic arithmetic - U. Rebstock: An Early hyperlink of the Arabic culture of sensible mathematics: The Kitab al -Thadhkira bi-usul al-hisab wa 'l-fara'id wa-'awliha wa-tashihiha - A. Djebbar: los angeles circulate des mathematiques entre l'Orient et l'Occident musulmans: Interrogations anciennes et components nouveaux - C. Burnett: Indian Numerals within the Mediterranean Basin within the 12th Century, with exact connection with the oEastern Formso - R. Franci: Jealous Husbands Crossing the River: an issue from Alcuin to Tartaglia - T. Levy: De l'arabe a l'hebreu: l. a. structure de l. a. litterature mathematique hebraique (XIIe-XVIe siecle) - B. van Dalen: Islamic and chinese language Astronomy below the Mongols: a Little-Known Case of Transmission - M. Bagheri: a brand new Treatise via al-Kashi at the melancholy of the obvious Horizon - A. Volkov: at the Origins of the Toan phap dai thanh (Great Compendium of Mathematical equipment) - M. Folkerts: Regiomontanus' position within the Transmission of Mathematical difficulties - D. Pingree: Philippe de l. a. Hire's Planetary Theories in Sanskrit. (Franz Steiner 2002)
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Additional info for From China to Paris: 2000 Years Transmission of Mathematical Ideas
Although the use of it = 3 in a number of cultures is hardly evidence of transmission, the situation for it = 10 is more complicated. We shall go into this example more fully later, and our point here is simply that there are no general rules for deciding between transmission and independent discovery. " Here, then, are seven methods for approximating.. ) 4 5 6 See (Jones 1997]. [Gupta 1985: 161. [Fowler & Robson 1998: 374-3751 suggest this. Ancient and Medieval Approximations to Irrational Numbers 33 Method 1.
Almagest VI 7. It is unclear why [Gupta 19731 ascribes Ptolemy's value to Apollonius. 65 (Heath 1921,1: 2341. 66 67 68 In his Tantra-sangraha and in his Golasara. [Gupta 1975: 31.
17. 28 1 + w + d = A = 12). 30 31 Ed. ]. ]. Ed. [Sesiano 1999). 22 Jens Hoyrup of the fact32 that ,2 = d 2 - w2 =(d+ w) (d - w) and finds [d - w] as 12l(d + w); w is then found as V2 ([1 + w) + [l - w]), and finally d as (d + w) - w. The third problem - identical with BM 34568, no. 10 apart from the numerical parameters - is solved in an algebraically more straightforward way (cf. note 23): first ((1 - iv)2) is found as 2d2 - (d+w)2, next w as '/2 ([1+w]-(1-w)), and ifinallyas (I+iv)-w. C All in all, these Greek problems might belong in the periphery of a cluster where the Demotic and Seleucid texts represent something closer to the core: 32 Figure 10.
From China to Paris: 2000 Years Transmission of Mathematical Ideas by Yvonne Dold-Samplonius, Benno van (Ed) Dalen