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Abu Bakr al-Hassar

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Al-Hassar or Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar (Arabic: أبو بكر محمد ابن عياش الحصَار‎)was a Muslim mathematician from Morocco, living in the 12th century. He is the author of two books Kitab al-bayan wat-tadhkar (Book of Demonstration and Memorization), a manual of calculation and Kitab al-kamil fi sinaat al-adad (Complete Book on the Art of Numbers), on the breakdown of numbers. The first book is lost and only a part of the second book remains.[1]

Al-Hassar developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar. This same fractional notation appeared soon after in the work of Fibonacci in the 13th century.


  1. ^ Selin, Helaine, ed. (1997). Encyclopaedia of the history of science, technology, and medicine in non western cultures. Boston: Kluwer Academic. p. 615. ISBN 0-7923-4066-3.

Further readingEdit

  • Suter, Heinrich, Beitraege zur Geschichte der Mathematik und Astronomie im Islam. Nachdruck seiner Schriften aus den Jahren 1892-1922. [Contributions to the history of mathematics and astronomy in Islam. Reprint of his works from the years 1892-1922]. Hrsg. von Fuat Sezgin. Baende 1 und 2. [Ed. by Fuat Sezgin. Volumes 1 and 2] Veroeffentlichungen des Institutes fuer Geschichte der Arabisch-Islamischen Wissenschaften. Reihe B: Nachdrucke, Abteilung Mathematik, Bd. 1 [Publications of the Institute for the History of Arabic-Islamic Sciences. Series B: Section Mathematics, vol. 1] Frankfurt am Main: Institut fuer Geschichte der Arabisch- Islamischen Wissenschaften an der Johann Wolfgang Goethe-Universitaet, 1986. Band I: xiii, 761 S.; Band II: x, 724 S.
  • Aballagh, M.; Djebbar, A. (1987). "Découverte d'un écrit mathématique d'al-Hassar (XIIe s.): Le livre I du Kamil". Historia Mathematica. 14 (2): 147–158. doi:10.1016/0315-0860(87)90018-8. ISSN 0315-0860.

External linksEdit

  • Prof. Paul Kunitzsch, Al-Hassâr's Kitâb al-Bayân and the Transmission of the Hindu-Arabic Numerals [1] retrieved 01-09-2010)
  • Manuscript of Kitâb al-bayân wa-l-tadhkâr, online by Library of the University of Pennsylvania, Philadelphia [2] (retrieved 01-09-2010)