Maths in the arab world introduction



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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”)



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





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.



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