*INTRODUCTION* ## Greeks ?? Europeans ## Conquests: Damascus, Jerusalem, ## Mesopotamia, Alexandria. ## 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**** **
## 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
## Al-Khwarizmi: father of Algebra **Kitab al-jabr wa'l-muqabala** – ‘algebra’
## 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)
## Solve the equation *x2+6x=7* ## Solve the equation *x2+6x=7* * *
## *(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-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. ## 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-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 2*k*-1(2*k* - 1) where 2*k* - 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.
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