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MATHS IN THE ARAB WORLD

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INTRODUCTION Greeks ?? Europeans Conquests: Damascus, Jerusalem, Mesopotamia, Alexandria. Arab territory: from India to Spain (including North Africa and South Italy) Library of Alexandria House of Wisdom(Beit al Hinka)

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Some translations Euclids Elements Ptolemys Almagest Aristotle, Apollonius, Archimedes, Heron, Diophantus and Indian writers.

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AL-KHWARIZMI Abu Abdallah Muhammad ibn Mūsā al-Jwārizmī Al-Khorezmi, al-Khwarizmi, Al-Khawarizmi, Al-Khawaritzmi or al-Khowarizmi

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Some notes about his biography 780 DC - Kharizm (south of Aral Sea) 850 DC - Bagdad 820 DC – Caliph Al'Mamun (House of Wisdom) Travels: Afghanistan, Turkey, Russia...

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Main works Maths, Astronomy, Astrology, Geography and History A page from Algebra

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Kitab al-jabr wa'l-muqabala – algebra -the most ancient book -method for solving linear and quadratic equations Reduction of the equations to one of six standard forms (b,c >0) : squares equal roots (ax 2 = bx) squares equal number (ax 2 = c) roots equal number (bx = c) squares and roots equal number (ax 2 + bx = c) squares and number equal roots (ax 2 + c = bx) roots and number equal squares (bx + c = ax 2 ) Al-Khwarizmi: father of Algebra

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Solve the equation x 2 +6x=7 total area: x 2 +6x+9 x 2 +6x+9 = 7+9 = 16 (x+3) 2 = 4 2 x = 1

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Algoritmi de numero Indorum (Latin translation) –numerical system India –zero

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The Arabic numeral system Different number systems were used simultaneously in the Arabic world over a long period of time. There were three different types of arithmetic (11th century): o counting on the fingers with the numerals written entirely in words o the sexagesimal system with numerals denoted by letters of the Arabic alphabet o the arithmetic of the Indian numerals

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al-Sizji (969) al-Biruni (1082) The biggest change was the fact that the 2 and the 3 have been rotated through 90º.

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The scribes therefore, instead of writing from right to left (the standard way that Arabic was written) wrote in lines from top to bottom.

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al-Banna al-Marrakushi ( beginning of the 14th century)

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Al-Haytham He was the first to attempt to classify all even perfect numbers as those of the form 2k-1(2k - 1) where 2k - 1 is prime. He is also the first person that we know to state Wilson's theorem: If p is prime then 1+(p-1)! is divisible by p.

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Trigonometry Al-Battani, Abul-Wafa, Ibn Yunus, Nasir al-Tusi The Arabs start their study with the idea of the Greeks and the idea of Hindus.At the end, they prefer the idea of the Hindus.

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