Al-Karaji
Encyclopedia
(c. 953 in Karaj
or Karkh
– c. 1029) was a 10th century Persian
Muslim mathematician
and engineer. His three major works are Al-Badi' fi'l-hisab (Wonderful on calculation), Al-Fakhri fi'l-jabr wa'l-muqabala (Glorious on algebra), and Al-Kafi fi'l-hisab (Sufficient on calculation).
Because al-Karaji's original works in Arabic are lost, it is not certain what his exact name was. It could either have been al-Karkhī, indicating that he was born in Karkh
, a suburb of Baghdad
, or al-Karajī indicating his family came from the city of Karaj
. He certainly lived and worked for most of his life in Baghdad, however, which was the scientific and trade capital of the Islam
ic world.
) but most regard him as more original, in particular for the beginnings of freeing algebra from geometry.
He systematically studied the algebra of exponents, and was the first to realise that the sequence x, x^2, x^3,... could be extended indefinitely; and the reciprocals 1/x, 1/x^2, 1/x^3,... . However, since for example the product of a square and a cube would be expressed, in words rather than in numbers, as a square-cube, the numerical property of adding exponents was not clear.
His work on algebra
and polynomial
s gave the rules for arithmetic operations for adding, subtracting and multiplying polynomials; though he was restricted to dividing polynomials by monomials.
He wrote on the binomial theorem
and Pascal's triangle
.
In a now lost work known only from subsequent quotation by al-Samaw'al Al-Karaji introduced the idea of argument by mathematical induction
. As Katz says
Karaj
Karaj is a city in and the capital of Karaj County, Alborz Province, Iran. At the 2006 census, its population was 1,377,450, in 385,955 families, , making it the fifth-largest city in Iran after Tehran, Mashhad, Isfahan and Tabriz.) It is situated west of Tehran, at the foothills of the Alborz...
or Karkh
Karkh
Karkh or Al-Karkh is historically the name of the western half of Baghdad, Iraq, or alternatively, the western shore of the river Tigris as it ran through Baghdad. The eastern shore is known as Al-Rasafa....
– c. 1029) was a 10th century Persian
Persian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...
Muslim mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and engineer. His three major works are Al-Badi' fi'l-hisab (Wonderful on calculation), Al-Fakhri fi'l-jabr wa'l-muqabala (Glorious on algebra), and Al-Kafi fi'l-hisab (Sufficient on calculation).
Because al-Karaji's original works in Arabic are lost, it is not certain what his exact name was. It could either have been al-Karkhī, indicating that he was born in Karkh
Karkh
Karkh or Al-Karkh is historically the name of the western half of Baghdad, Iraq, or alternatively, the western shore of the river Tigris as it ran through Baghdad. The eastern shore is known as Al-Rasafa....
, a suburb of Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...
, or al-Karajī indicating his family came from the city of Karaj
Karaj
Karaj is a city in and the capital of Karaj County, Alborz Province, Iran. At the 2006 census, its population was 1,377,450, in 385,955 families, , making it the fifth-largest city in Iran after Tehran, Mashhad, Isfahan and Tabriz.) It is situated west of Tehran, at the foothills of the Alborz...
. He certainly lived and worked for most of his life in Baghdad, however, which was the scientific and trade capital of the Islam
Islam
Islam . The most common are and . : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...
ic world.
Work
Al-Karaji wrote on mathematics and engineering. Some consider him to be merely reworking the ideas of others (he was influenced by DiophantusDiophantus
Diophantus of Alexandria , sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost...
) but most regard him as more original, in particular for the beginnings of freeing algebra from geometry.
He systematically studied the algebra of exponents, and was the first to realise that the sequence x, x^2, x^3,... could be extended indefinitely; and the reciprocals 1/x, 1/x^2, 1/x^3,... . However, since for example the product of a square and a cube would be expressed, in words rather than in numbers, as a square-cube, the numerical property of adding exponents was not clear.
His work on algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s gave the rules for arithmetic operations for adding, subtracting and multiplying polynomials; though he was restricted to dividing polynomials by monomials.
He wrote on the binomial theorem
Binomial theorem
In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with , and the coefficient a of...
and Pascal's triangle
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
.
In a now lost work known only from subsequent quotation by al-Samaw'al Al-Karaji introduced the idea of argument by mathematical induction
Mathematical induction
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers...
. As Katz says
See also
- Mathematics in medieval Islam
- Science in medieval Islam
- List of Iranian scientists