Al-Karaji Explained

Abū Bakr al-Karajī
Caption:Diagrams from Al-Karaji's work on "hidden waters"
Birth Date:953
Birth Place:Karaj,[1] Persia
Nationality:Persian
Main Interests:Mathematics, Engineering

(Persian: ابو بکر محمد بن الحسن الکرجی; c. 953  - c. 1029) was a 10th-century Persian[2] [3] [4] mathematician and engineer who flourished at Baghdad. He was born in Karaj,[1] a city near Tehran. His three principal surviving works are mathematical: 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).

Work

Al-Karaji wrote on mathematics and engineering. Some consider him to be merely reworking the ideas of others (he was influenced by Diophantus) but most regard him as more original,[5] in particular for the beginnings of freeing algebra from geometry. Among historians, his most widely studied work is his algebra book al-fakhri fi al-jabr wa al-muqabala, which survives from the medieval era in at least four copies.

He expounded the basic principles of hydrology[6] and this book reveals his profound knowledge of this science and has been described as the oldest extant text in this field.[7] [8] [9]

He systematically studied the algebra of exponents, and was the first to define the rules for monomials like x,x²,x³ and their reciprocals in the cases of multiplication and division. 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.[10]

His work on algebra and polynomials gave the rules for arithmetic operations for adding, subtracting and multiplying polynomials; though he was restricted to dividing polynomials by monomials.

F. Woepcke was the first historian to realise the importance of al-Karaji's work and later historians mostly agree with his interpretation. He praised Al-Karaji for being the first who introduced the theory of algebraic calculus.[11]

Al-Karaji gave the first formulation of the binomial coefficients and the first description of Pascal's triangle.[12] [13] [14] He is also credited with the discovery of the binomial theorem.[15] In a now lost work known only from subsequent quotation by al-Samaw'al, Al-Karaji introduced the idea of argument by mathematical induction.[16] As Katz says

See also

References and external links

Notes and References

  1. PAZWASH. HORMOZ. MAVRIGIAN. GUS. 1986. The Contributions of Karaji—Successor to al-Khwarizmi. The Mathematics Teacher. 79. 7. 538–541. 10.5951/MT.79.7.0538 . 27965055 . 0025-5769.
  2. Web site: Muhammad Al-Karaji: A Mathematician Engineer from the Early 11th Century Muslim Heritage. www.muslimheritage.com. en. 2018-08-10. Of Persian origin, he spent an important part of his scientific life in Baghdad where he composed ground breaking mathematical books..
  3. Book: Selin, Helaine . Encyclopaedia of the history of science, technology, and medicine in non-western cultures . Springer . Berlin New York . 2008 . 9781402049606 . 131 . Al-Karajī Abū Bakr Muh.ammad was a Persian mathematician and engineer..
  4. Book: Meri. Josef W.. Medieval Islamic Civilization, Volume 1 An Encyclopedia. January 2006. Routledge. 978-0-415-96691-7. 32. During the tenth century CE, the Iranian mathematician al-Karaji (...).
  5. Web site: al-Karaji - Biography. Maths History.
  6. Book: Hydrology: Principles and Processes. Robinson. M.. Ward. R. C.. 2017-02-15. IWA Publishing. 9781780407289. en. 19.
  7. http://www.muslimheritage.com/article/muhammad-al-karaji#sec_5/ Muslim Heritage, Mohammed Abattouy
  8. Book: Sorkhabi, Rasoul. Tectonic Evolution, Collision, and Seismicity of Southwest Asia: In Honor of Manuel Berberian's Forty-Five Years of Research Contributions. 2017-12-21. Geological Society of America. 9780813725253. en. 37.
  9. Niazi. Kaveh. 2016-01-01. Karajī's Discourse on Hydrology. Oriens. en. 44. 1–2. 44–68. 10.1163/18778372-04401003. 0078-6527. The hydrological concepts presented in Inbāṭ al-miyāh al-khafīya, Muḥammad Karajī’s 11th century text on the construction of the qanāt, contain unexpected premises and theories that set this text apart from its contemporaries. Even when not straying far from the Aristotelian cosmology of the medieval world, Karajī’s hydrological discussions often represent a fresh take on the common scientific wisdom regarding the flow of water at and near the earth’s surface. .
  10. Katz, History of Mathematics, first edition, p237
  11. https://books.google.com/books?id=CdIAAwAAQBAJ&q=al+karaji+first+formulation+of+the+binomial+theorem%2F&pg=PA26 "You Have Got to Know...Mathematics"
  12. Book: From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of J.L. Berggren. Sidoli. Nathan. Brummelen. Glen Van. 2013-10-30. Springer Science & Business Media. 9783642367366. en. 54.
  13. Book: Selin, Helaine. Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. 2008-03-12. Springer Science & Business Media. 9781402045592. en. 132.
  14. https://books.google.com/books?id=vSkClSvU_9AC&pg=PA62 The Development of Arabic Mathematics Between Arithmetic and Algebra - R. Rashed
  15. Web site: THE BINOMIAL THEOREM : A WIDESPREAD CONCEPT IN MEDIEVAL ISLAMIC MATHEMATICS. core.ac.uk. 2019-01-08. 401.
  16. Web site: Abattouy. Mohammed. 2009. Muhammad Al-Karaji: A Mathematician Engineer from the Early 11th Century. Muslim heritage. He was also the first to use the method of proof by mathematical induction to prove his results, which he also used to prove the sum formula for integral cubes, an important result in integral calculus..

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