# MATHS IN THE ARAB WORLD

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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). - PowerPoint PPT Presentation

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• MATHS IN THE ARAB WORLD

• INTRODUCTIONGreeks ?? 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 translationsEuclids Elements

Ptolemys Almagest

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

• AL-KHWARIZMIAbu Abdallah Muhammad ibn Ms al-Jwrizm Al-Khorezmi, al-Khwarizmi, Al-Khawarizmi,Al-Khawaritzmi or al-Khowarizmi

• Some notes about his biography780 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 algebrathe most ancient bookmethod 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 Algebra

• Solve the equation x2+6x=7

total area: x2+6x+9 x2+6x+9 = 7+9 = 16(x+3) 2 = 42x = 1

• Algoritmi de numero Indorum(Latin translation)

numerical system Indiazero

• The Arabic numeral systemDifferent 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 alphabetthe 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 90.

• 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-HaythamHe 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.

• TrigonometryAl-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.

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