2INTRODUCTION Greeks ?? Europeans Conquests: Damascus, Jerusalem, Mesopotamia, Alexandria.Arab territory: from India toSpain (including North Africaand South Italy)Library of Alexandria House of Wisdom(“Beit al Hinka”)
3Some translations Euclid’s Elements Ptolemy’s Almagest Aristotle, Apollonius, Archimedes, Heron, Diophantus and Indian writers.
5AL-KHWARIZMI Abu Abdallah Muhammad ibn Mūsā al-Jwārizmī Al-Khorezmi, al-Khwarizmi, Al-Khawarizmi,Al-Khawaritzmi or al-Khowarizmi
6Some notes about his biography 780 DC - Kharizm (south of Aral Sea)850 DC - Bagdad820 DC – Caliph Al'Mamun (House of Wisdom)Travels: Afghanistan, Turkey, Russia...
7Main works Maths, Astronomy, Astrology, Geography and History A page from Algebra
8Al-Khwarizmi: father of Algebra Kitab al-jabr wa'l-muqabala – ‘algebra’the most ancient bookmethod for solving linear and quadratic equationsReduction 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)
9Solve the equation x2+6x=7 total area: x2+6x+9x2+6x+9 = 7+9 = 16(x+3) 2 = 42x = 1
10Algoritmi de numero Indorum (Latin translation) numerical systemIndiazero
11The 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 wordsthe sexagesimal system with numerals denoted by letters of the Arabic alphabetthe arithmetic of the Indian numerals
12al-Sizji (969) al-Biruni (1082) The biggest change was the fact that the 2 and the 3 have been rotated through 90º.
13The scribes therefore, instead of writing from right to left (the standard way that Arabic was written) wrote in lines from top to bottom.
14al-Banna al-Marrakushi (beginning of the 14th century)
15Al-HaythamHe 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.
16Al-Battani, Abu’l-Wafa, Ibn Yunus, Nasir al-Tusi TrigonometryAl-Battani, Abu’l-Wafa, Ibn Yunus, Nasir al-TusiThe 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.