Root extraction by Al-Kashi and Stevin

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• 作者：Nuh Aydin ; Lakhdar Hammoudi
• 刊名：Archive for History of Exact Sciences
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：69
• 期：3
• 页码：291-310
• 全文大小：613 KB
• 参考文献：Al-Kashi, G.J.M. 1969. Miftah al-Hisab (edition, and commentary by Amad Sa’id al-Dimirdash and Muammad Hamdi al-Hifni al-Shaykh). Cairo: Dar al-Katib al-Arabi.
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  Dakhel, A. 1960. In The extraction of the n-th root in the sexagesimal notation. A study of chapter 5, treatise 3 of Miftah al-hisab, ed. W.A. Hijab, and E.S. Kennedy. Beirut: American University of Beirut.
  Hogendijk, J.P. 2009. Al-Kashi’s determination of \(\pi \) to 16 decimals in an old manuscript. Zeitschrift fr Geschichte der arabisch-islamischen Wissenschaften 18: 73-52.MathSciNet
  Luckey, P. 1951. Die Rechnenkunst bei Gamsid b. Masud Al-Kasi. Wiesbaden.
  O’Conner J. J., and E. F. Robertson. 1999. The MacTutor history of mathematics archive. http://?www-history.?mcs.?st-andrews.?ac.?uk/?index.?html
  Rashed, R. 1978. L’Extraction de la Racine \(n^{{\rm i\grave{e}me}}\) et l’Invention des Fractions Décimales (\(XI^e- XII^e\) Siècles). Archive for History of Exact Sciences 18(3): 191-43.MATH MathSciNet
  Rashed, R. 1994. The development of Arabic mathematics between arithmetic and algebra (trans: Armstrong, A.F.W.). Dordrecht: Kluwer.
  Saidan, A. 1966. The earliest extant arabic arithmetic. Isis 57(194): 475-90.View Article
  Saidan, A. 1978. The arithmetic of al-Uqlidisi: The story of Hindu–Arabic arithmetic as told in Kitab al-Fusul fi al-Hisab al-Hindi (trans and annotated: Saidan, A.S.). Dordrecht: Reidel Publishing.
  Stevin, S. L’arithmétique, corrected and augmented by Albert Girard, De l’imprimerie des Elzeviers, 1625. http://?www.?arcliive.?org/?details/?laritlimetiqvede?sOOstev .
  Taani, O. 2014. Multiple paths to mathematics practice in Al-Kashis key to arithmetic. Science & Education 23(1): 125-41.View Article
  
• 作者单位：Nuh Aydin (1)
  Lakhdar Hammoudi (2)
  
  1. Department of Mathematics and Statistics, Kenyon College, 201 N. College Rd, Gambier, OH, 43022, USA
  2. Department of Mathematics, Ohio University, 101 University Drive, Chillicothe, OH, 45601, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  History of Mathematics
  Mathematics
  Physics
  Mathematical and Computational Physics
  Astronomy
  Astrophysics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0657

文摘

In this paper, we study the extraction of roots as presented by Al-Kashi in his 1427 book “Key to Arithmetic-and Stevin in his 1585 book “Arithmetic- In analyzing their methods, we note that Stevin’s technique contains some flaws that we amend to present a coherent algorithm. We then show that the underlying algorithm for the methods of both Al-Kashi and Stevin is the same.