MATHS IN MATHS IN THE ARAB THE ARAB

WORLDWORLD

INTRODUCTION

• Greeks ?? EuropeansConquests: Damascus, Jerusalem,Mesopotamia, Alexandria.Arab territory: from India toSpain (including North Africaand 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.

A lgeb ra A rith m etic T rigo n o m etry

A rab ic m athem atic ians

AL-KHWARIZMIAL-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 worksMaths, Astronomy, Astrology, Geography

and History

A page from 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)

Al-Khwarizmi: father of Al-Khwarizmi: father of AlgebraAlgebra

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 counting on the fingers with the numerals written entirely in words

o the sexagesimal system with numerals denoted by letters of the Arabic alphabet

o 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.