Abu Bakr al-Karaji

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Images from al-Karaji's work on the development of hidden waters.

Abu Bakr Muhammad ibn al-Husain al-Karaji ( Arabic أبو بكر محمد بن الحسين الكرجي, DMG Abū Bakr Muḥammad b. al-Ḥusain al-Karaǧī , also Karaji , or al-Karchi  /الكرخي / al-Karḫī , also al-Karkhi ; also al-Hasan  /الحسن / al-Ḥasan ; * probably in the second half of the 10th century in Karaj ; † around 1020 ) was a Persian mathematician and engineer.

biography

Abu Bakr al-Karaji's exact date of birth is unknown. His place of birth was suspected for a long time in the Baghdad administrative district of Karkh, until a study by the Italian Islamic scholar Giorgio Levi Della Vida published in 1934 plausibly presented the Iranian city of Karaj as the place of birth instead. There is also only fragmentary information about his later life, mainly from his books. He worked as an engineer in the mountainous regions of Iran and later traveled to Baghdad to take on an official role there. There he also wrote his mathematical works around 1012. Presumably al-Karaji left Baghdad after the murder of Wezir Fachr al-Mulk, to whom his treatise al-Fachrī is also dedicated. He returned to Karaj where he wrote his treatise on hydrology on the orders of the ruler Falak al-Ma'ali Manuchihr. He probably died between 1019 and 1029.

Services

Al-Karaji wrote several treatises on mathematics, three of which have survived : al-Badīʿ fī l-hisāb (Wonderful Arithmetic), al-Fachrī fī l-Jabr wa-l-muqābala (The Glory of Algebra), and al- Kāfī fī l-hisāb (Sufficient information on arithmetic). He mainly used the works of Greek mathematicians, Indian works were hardly used. Building on the work of Diophantos of Alexandria , he developed new solution methods for quadratic equations . He was also able to show that some equations of a higher degree can be reduced to quadratic equations.

His two-part work al-Fachrī fī l-jabr wa-l-muqābala was strongly influenced by the book Arithmetika by Diophantus. Furthermore, he is based on statements of the mathematician Abu Kamil . In al-Fachrī he deals with solutions to quadratic equations. The proof of a sum formula for the sum of successive cubes goes back to al-Karaji. He used full induction .

The second part of the work contains 254 problems based on definite and indefinite equations. Some of these tasks were reused by Leonardo Fibonacci , Leonardo da Vinci, and Gerolamo Cardano without naming the author.

Another important achievement of al-Karaji is the development of the method of the penalty test , which he described for the first time in al-Kāfī fī l-hisāb (Sufficient Information on Arithmetic).

Some of his results are only available in the writings of other Islamic authors (e.g. as-Samaw'al ), including his introduction of Pascal's triangle .

Al-Karaji wrote the hydrological textbook entitled Inbat al-miyah al-khafiya (On the Development of Hidden Waters), which published important geological and hydrogeological theories that had been ascribed to Avicenna and Biruni until the 1970s .

literature

  • Hans Wußing : 6000 years of mathematics: a cultural-historical journey through time - 1. From the beginnings to Leibniz and Newton, from the counting stone to the computer. 2008, ISBN 978-3-54077-189-0
  • M. Nadji: The oldest textbook on hidden waters. In: Borsuye. Journal for Medicine a. Culture 10, 1998, 39, pp. 12-14
  • Charles C. Gillispie (Editor): Dictionary of Scientific Biography . Charles Scribner's Sons, New York 1970–1980, 15 volumes and an index volume, ISBN 0-684-10114-9 , Supplement II, edited by Frederic Lawrence Holmes, 2 volumes, 1990, ISBN 0-684-16962-2 (ISBN of the complete edition ).
  • Herbert Pieper: Heureka - I've found it, 55 historical tasks in elementary mathematics , VEB Deutscher Verlag der Wissenschaften, Berlin 1988, ISBN 3-326-00364-1 .
  • Alireza Djafari Naini: History of number theory in the Orient, in the Middle Ages and at the beginning of the modern era with special emphasis on Persian mathematicians. , Verlag Klose & Co, Braunschweig, 1982
  • Johannes Tropfke, Kurt Vogel, Karin Reich , Helmuth Gericke: History of elementary mathematics. Arithmetic and algebra. Verlag Walter de Gruyter, 1980, ISBN 3-11-004893-0 .
  • Jacques Sesiano: Le traitement des équations indéterminées dans le Badīʿ fī 'l-Ḥisāb d'Abū Bakr Al-Karajī , Archive for History of Exact Sciences, vol. 17, No. 4, December 29, 1977, pp. 297-379
  • Kurt Vogel: An indefinite problem of al-Karaǧī in arithmetic books of the Occident , Sudhoff's archive. Journal for the History of Science 61, pp. 66–74
  • Roshdi Rashed : Le travaux perdus de Diophante in Revue d'Histoire des Sciences , 28th Paris 1975
  • Fuat Sezgīn: History of Arabic Literature. Volume 5 Mathematics, publications of the Institute for the History of the Arab-Islamic Sciences, Verlag EJ Brill 1974, ISBN 978-9004041530
  • SN Davis: Discussion of "Exploration the hidden water" In: Ground Water 10, 1972, No. 7
  • M. Nadji: Karadji's Development of Hidden Waters. In: Journal of the German Geological Society 123, 1972, 1, pp. 1–13
  • Giorgio Levi della Vida: Appunti e quesiti di storia letteraria araba. 4. Due nuove opere del matematico al-Karagi (al-Karkhi) , Rivista degli Studi Orientali (Roma) vol. 14, 1934, pp. 249-264
  • Moritz Cantor : Lectures on the history of mathematics. Second volume. From 1200–1668. , Leipzig, BG Teubner 1900
  • Franz Woepcke (Ed.): Extrait du Fakhri, par Abou Bekr Mohammed Ben al Haçan al Karkhi. , Paris, 1853 ( online )

Web links

Commons : Abu Bakr al-Karaji  - Collection of images, videos and audio files

Notes and individual references

  1. ^ Biographies of famous mathematicians
  2. ↑ Vida: Due nuove opere del matematico al-Karagi (al-Karkhi) , 1934, pp. 249-264
  3. ↑ Sesiano: Le traitement of Equations indéterminées dans le Badī' fī 'l-Hisab d'Abu Bakr Al-Karajī , 1977, pp 297-379
  4. ↑ a b c Naini: History of number theory in the Orient , p. 20
  5. ↑ a b Sezgīn: History of Arabic literature. , Vol. 5, p. 325 ff.
  6. ↑ Sezgin: history of Arab writing , vol 5, p 43rd
  7. ↑ Johannes Tropfke, Kurt Vogel, Karin Reich , Helmuth Gericke: History of Elementary Mathematics. Arithmetic and algebra. Verlag Walter de Gruyter, 1980, ISBN 3-11-004893-0 .
  8. ↑ Rashed: Le travaux perdus de Diophante , pp. 3-30
  9. ↑ Naini: History of number theory in the Orient. , P. 121ff
  10. ↑ Hans Wußing : 6000 years of mathematics: a cultural-historical journey through time 1. From the beginnings to Leibniz and Newton, from counting stone to computer. 2008, ISBN 978-3-54077-189-0
  11. ↑ Naini: History of number theory in the Orient. , P. 170ff
  12. ↑ Naini: History of Number Theory in the Orient , p. 104
  13. ^ Pieper: Heureka , pp. 59–60
  14. ^ Vogel: An indefinite problem of al-Karaǧī in arithmetic books of the West
  15. ↑ Naini: History of Number Theory in the Orient , pp. 32–33
  16. ↑ Nadji: Karadji's Development of Hidden Waters. , 1972, 1, pp. 1-13
  17. ↑ Nadji: The oldest textbook on hidden waters. , 1998, pp. 12-14
  18. ↑ Davis: Discussion of "Exploration the hidden water," 1972, No. 7
personal data
SURNAME Karaji, Muhammad al-
ALTERNATIVE NAMES Karaji, Abu Bakr Muhammad ibn al-Husain al-; Karaǧī, Muḥammad Ibn-al-Ḥasan al-
BRIEF DESCRIPTION Persian mathematician and engineer
DATE OF BIRTH uncertain: between 950 and 1000
PLACE OF BIRTH Karaj
DATE OF DEATH uncertain: around 1020