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.

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): 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.

Al-Battani, Abu’l-Wafa, Ibn Yunus, Nasir al-Tusi 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.