Conf_mahdi_1

Conf_mahdi_1 - mathematics Mahdi ABDELJAOUAD From arithmetic to algebra Part 1 Summary Introduction Algebra Conclusion Palerme 25-26 novembre 2003

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Some elements in the history of Arab  mathematics  Mahdi ABDELJAOUAD From arithmetic to algebra Part 1
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Palerme, 25-26 novembre 2003 2 Summary Introduction  Domains studied by Arabs Arithmetic and number theory Algebra Conclusion
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Palerme, 25-26 novembre 2003 3 Quick Chronology of Islam 622 : First year of Arabic Calendar 632 : Death of Mohamed, the Prophet 633 – 640 : conquest of Syria and Mesopotamia 639 – 646 : conquest of Egypt. 687 – 702 : conquest of North Africa. 701 – 716 : conquest of Spain (Andalusia). 640 – 750 : Reign of the Ommayads (Damascus) 762 – 1258 : Reign the Abbassids. (Baghdad) 1055 : Turks take over Baghdad 1258 : Mongols take over Baghdad. 1492 : Christians take over Grenada and arrive in America.
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Palerme, 25-26 novembre 2003 4
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Palerme, 25-26 novembre 2003 5 From 750 up to 900 
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Palerme, 25-26 novembre 2003 6 From 900 up to 1000 
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Palerme, 25-26 novembre 2003 7 From 1100 up to 1300 
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Palerme, 25-26 novembre 2003 8 From 1300 up to 1500 
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Palerme, 25-26 novembre 2003 9 Subjects studied by Arab mathematicians Geometry  : Thabit ibn Qurra – Omar al-Khayyam – Ibn  al-Haytham. Sciences of numbers   1. Indian numeration  : al-Uqludisi.   2. Business arithmetic  : Abu l-Wafa. 3. Algebra  : al-Khawarizmi  4. Decimal numbers  : al-Kashi 5. Combinatorics  : Ibn al-Mun c im Trigonometry  : Nasir ad-Dine at-Tusi Astronomy  : al-Biruni Science of music  : al-Farabi.
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Palerme, 25-26 novembre 2003 10 Science of numbers « al – arithmétika » and « c Ilm al-hisāb » The first one is speculative or theoretical and is interested to abstract numbers and to pytagorical and euclidian arithmetic. The second one is active or practical and is interested to concrete numbers and to the needs of merchants.
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Palerme, 25-26 novembre 2003 11 Speculative arithmetic Inspired from Aristotle philosophy Two approaches : 1. Euclid’s Elements Books VII – VIII and IX 2. Pythagoras through Nicomachus of Gerase’s Introduction to Arithmetic . Thabit ibn Qurra (d.901) Bagdad (a star worshipper)
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Palerme, 25-26 novembre 2003 12 Types of active arithmetic 1 . Al-hisāb al-hawā’i (air calculus) Based solely on memory Rethorical calculus uses only words in the text and no symbols. It is digital : calculus uses fingers to compute and to do operations. It uses unitary and sexagesimal fractions How to solve problems: rule of three – algebra A chapter on geometric mensurations A great number of practical problems
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Palerme, 25-26 novembre 2003 13 Abu'l-Wafa (d.998) Bagdad Book on what Is necessary from the science of arithmetic for scribes and businessmen This book : ... comprises all that an experienced or novice, subordinate or chief in arithmetic needs to know, the art of civil servants, the employment of land taxes and all kinds of business needed in administrations, proportions, multiplication,
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This note was uploaded on 11/11/2011 for the course MATH 110 taught by Professor Staff during the Winter '08 term at BYU.

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Conf_mahdi_1 - mathematics Mahdi ABDELJAOUAD From arithmetic to algebra Part 1 Summary Introduction Algebra Conclusion Palerme 25-26 novembre 2003

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