Al-Karaji
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Abu Bakr Muhammad ibn al-Hasan al-Karaji (Arabic: ابو بكر محمد بن الحاسب الكرجي) (c.953 –c.1029), was a Muslim mathematician and engineer of Persian background. 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). He was born in the city of Karaj.
Because al-Karaji's original works in Arabic are lost, it is not certain what his exact name was. An older, now largely discarded, theory identifies him as al-Husain al-Karkhi (Arabic: الحسين الكرخى), indicating that he was born in Karkh, near Baghdad. He certainly lived and worked for most of his life in Baghdad, however, which was the scientific and trade capital of the Islamic world.
Al-Karaji was an engineer and mathematician of the highest calibre. His enduring contributions to the field of mathematics and engineering are still recognised today in the form of the table of binomial coefficients, its formation law:
- [ = + ]
- [(a+b)^n=\sum_^na^kb^]
Al-Karaji wrote about the work of earlier mathematicians, and he is now regarded as the first person to free algebra from geometrical operations, that were the product of Greek arithmetic, and replace them with the type of operations which are at the core of algebra today. His work on algebra and polynomials, gave the rules for arithmetic operations to manipulate polynomials. Historian of mathematics F. Woepcke in Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi (Paris, 1853), praised Al-Karaji for being the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle. He also made use of the induction method to prove his results.
See also
References and external links
- J. Christianidis. Classics in the History of Greek Mathematics, p. 260
- Carl R. Seaquist, Padmanabhan Seshaiyer, and Dianne Crowley. ["Calculation across Cultures and History"] (Texas College Mathematics Journal 1:1, 2005; pp 15–31) [PDF]
- Matthew Hubbard and Tom Roby. ["The History of the Binomial Coefficients in the Middle East"] (from "Pascal's Triangle from Top to Bottom")
- John J. O'Connor and Edmund F. Robertson. [] at the MacTutor History of Mathematics archive.
- Fuat Sezgin. Geschichte des arabischen Schrifttums (1974, Leiden: E. J. Brill)
- James J. Tattersall. Elementary Number Theory in Nine Chapters, p. 32
- Mariusz Wodzicki. ["Early History of Algebra: a Sketch"] (Math 160, Fall 2005) [PDF]
- ["al-Karaji"] — Encyclopædia Britannica Online (4 April 2006)
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