By Yvonne Dold-Samplonius;Benno van (Ed) Dalen

ISBN-10: 3515082239

ISBN-13: 9783515082235

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 middle der Rockefeller beginning 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: ok. Vogel: A Surveying challenge Travels from China to Paris - J. Hoyrup: Seleucid techniques within the Babylonian oAlgebraico culture and their relatives out of the country - J. L. Berggren: a few old 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 global - J. P. Hogendijk: Anthyphairetic Ratio thought 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 move 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 distinctive 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 los angeles 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 noticeable Horizon - A. Volkov: at the Origins of the Toan phap dai thanh (Great Compendium of Mathematical tools) - M. Folkerts: Regiomontanus' position within the Transmission of Mathematical difficulties - D. Pingree: Philippe de los angeles 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 (Boethius. Texte und Abhandlungen zur Geschichte der Mathematik und der Naturwissenschaften)

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01 = 9 1 . . 1 · · · 10 . . 01 10 . . 01 . . 10 . . 01 . 81 9 8 9 8 8 8 8 8 The second and third factors are composed of 9 units, so the sum of their digits is divisible by 9, that is, each is a multiple of 9. Hence 1081 − 1 is divisible by 93 = 729, as is 1081n − 1 for any n. 6. In the isosceles triangle ABC (AC = BC) point O is the circumcenter, I the incenter, and D lies on BC so that lines OD and BI are perpendicular. Prove that ID and AC are parallel. e. O = I) the statement is obvious.

Let i = 1 if xi occurs in A but not in B, −1 if xi occurs in B but not in A, and 0 otherwise; then i xi is divisible by n3 . 47 3. Let x, y be real numbers. Show that if the set {cos(nπx) + cos(nπy)|n ∈ N} is finite, then x, y ∈ Q. Solution: Let an = cos nπx and bn = sin nπx. Then (an + bn )2 + (an − bn )2 = 2(a2n + b2n ) = 2 + (a2n + b2n ). If {an + bn } is finite, it follows that {an − bn } is also a finite set, and hence that {an } is finite, since an = 1 [(an + bn ) + (an − bn )], 2 and similarly {bn } is finite.

E. N ≤ 77. In particular, if N = 16000, this cannot be the case. 5. Show that in the arithmetic progression with first term 1 and ratio 729, there are infinitely many powers of 10. Solution: We will show that for all natural numbers n, 1081n − 1 is divisible by 729. 9 = 9 . . 9 · · · 10 . . 01 10 . . 01 . . 10 . . 01 = 9 1 . . 1 · · · 10 . . 01 10 . . 01 . . 10 . . 01 . 81 9 8 9 8 8 8 8 8 The second and third factors are composed of 9 units, so the sum of their digits is divisible by 9, that is, each is a multiple of 9.

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From China to Paris: 2000 Years Transmission of Mathematical Ideas (Boethius. Texte und Abhandlungen zur Geschichte der Mathematik und der Naturwissenschaften) by Yvonne Dold-Samplonius;Benno van (Ed) Dalen


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