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MATHS IN THE ARAB WORLD 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”) Some translations • Euclid’s Elements • Ptolemy’s Almagest • Aristotle, Apollonius, Archimedes, Heron, Diophantus and Indian writers. Arabic mathematicians Algebra Arithmetic Trigonometry AL-KHWARIZMI Abu Abdallah Muhammad ibn Mūsā al-Jwārizmī Al-Khorezmi, al-Khwarizmi, Al-Khawarizmi, Al-Khawaritzmi or al-Khowarizmi 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... Main works Maths, Astronomy, Astrology, Geography and History A page from Algebra Al-Khwarizmi: father of Algebra 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 (ax2 = bx) squares equal number (ax2 = c) roots equal number (bx = c) squares and roots equal number (ax2 + bx = c) squares and number equal roots (ax2 + c = bx) roots and number equal squares (bx + c = ax2) Solve the equation x2+6x=7 total area: x2+6x+9 x2+6x+9 = 7+9 = 16 (x+3) 2 = 42 x=1 Algoritmi de numero Indorum (Latin translation) – numerical system India – zero 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 o o counting on the fingers with the numerals written entirely in words the sexagesimal system with numerals denoted by letters of the Arabic alphabet the arithmetic of the Indian numerals • al-Sizji (969) • al-Biruni (1082) The biggest change was the fact that the 2 and the 3 have been rotated through 90º. • The scribes therefore, instead of writing from right to left (the standard way that Arabic was written) wrote in lines from top to bottom. • al-Banna al-Marrakushi (beginning of the 14th century) 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. Trigonometry Al-Battani, Abu’l-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.