maths in the arab world. introduction greeks ?? europeans conquests: damascus, jerusalem,...
TRANSCRIPT
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.