Transcript AL-KHWARIZMI

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.
Arabic mathematicians
Algebra
Arithmetic
Trigonometry
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
A page from Algebra
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
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
o
o
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-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.