MATHS%20IN%20THE%20ARAB%20WORLD

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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

• Euclids Elements
• Ptolemys Almagest
• Aristotle, Apollonius, Archimedes, Heron,
  Diophantus and Indian writers.

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AL-KHWARIZMI

• Abu Abdallah Muhammad ibn Musa al-Jwarizmi
• 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 gt0)
• 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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• Solve the equation x26x7

• total area x26x9
• x26x9 79 16
• (x3) 2 42
• x 1

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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, Abul-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.