Maths in the arab world introduction

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

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

• Solve the equation x2+6x=7

• 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-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 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.