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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”).

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MATHS IN THE ARAB WORLD

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Maths in the arab world l.jpg

MATHS IN THE ARAB WORLD


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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”)


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Some translations

  • Euclid’s Elements

  • Ptolemy’s Almagest

  • Aristotle, Apollonius, Archimedes, Heron, Diophantus and Indian writers.


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AL-KHWARIZMI

Abu Abdallah Muhammad ibn Mūsā al-Jwārizmī

Al-Khorezmi, al-Khwarizmi, Al-Khawarizmi,

Al-Khawaritzmi or al-Khowarizmi


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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...


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Main worksMaths, Astronomy, Astrology, Geography and History

A page from Algebra


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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)


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  • total area: x2+6x+9

  • x2+6x+9 = 7+9 = 16

  • (x+3) 2 = 42

  • x = 1

Solve the equation x2+6x=7


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Algoritmi de numero Indorum

(Latin translation)

  • numerical system

    India

  • zero


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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


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  • al-Sizji (969)

  • al-Biruni (1082)

    The biggest change was the fact that the 2 and the 3 have been rotated through 90º.


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  • The scribes therefore, instead of writing from right to left (the standard way that Arabic was written) wrote in lines from top to bottom.


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  • al-Banna al-Marrakushi (beginning of the 14th century)


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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.


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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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