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Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (Persian: ابوالوفا بوزجانی or بوژگانی)[1] (10 June 940 – 15 July 998)[2] was a Persian[3][4][5] mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text.

Abu al-Wafa' al-Buzjani
Born(940-06-10)June 10, 940
Buzhgan, Iran
DiedJuly 15, 998(998-07-15) (aged 58)
Baghdad
Academic background
InfluencesAl-Battani
Academic work
EraIslamic Golden Age
Main interestsMathematics and Astronomy
Notable worksAlmagest of Abū al-Wafā'
Notable ideas
  • Tangent function
  • Law of sines
  • Several trigonometric identities
InfluencedAl-Biruni, Abu Nasr Mansur

He is also credited with compiling the tables of sines and tangents at 15 ' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc.[2] His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived.


Life


He was born in Buzhgan, (now Torbat-e Jam) in Khorasan (in today's Iran). At age 19, in 959 AD, he moved to Baghdad and remained there until his death, in 998.[2] He was a contemporary of the distinguished scientists Abū Sahl al-Qūhī and Al-Sijzi who were in Baghdad at the time and others like Abu Nasr Mansur, Abu-Mahmud Khojandi, Kushyar Gilani and Al-Biruni.[6] In Baghdad, he received patronage by members of the Buyid court.[7]


Astronomy


Abu Al-Wafa' was the first to build a wall quadrant to observe the sky.[6] It has been suggested that he was influenced by the works of Al-Battani as the latter describes a quadrant instrument in his Kitāb az-Zīj.[6] His use of tangent helped to solve problems involving right-angled spherical triangles, and developed a new technique to calculate sine tables, allowing him to construct more accurate tables than his predecessors.[7]

In 997, he participated in an experiment to determine the difference in local time between his location, Baghdad, and that of al-Biruni (who was living in Kath, now a part of Uzbekistan).[8] The result was very close to present-day calculations, showing a difference of approximately 1 hour between the two longitudes. Abu al-Wafa is also known to have worked with Abū Sahl al-Qūhī, who was a famous maker of astronomical instruments.[7] While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni.[7]


Almagest


Among his works on astronomy, only the first seven treatises of his Almagest (Kitāb al-Majisṭī) are now extant.[9] The work covers numerous topics in the fields of plane and spherical trigonometry, planetary theory, and solutions to determine the direction of Qibla.[6][7]


Mathematics


He defined the tangent function, and he established several trigonometric identities such as in their modern form, where the Ancient Greek mathematicians had expressed the equivalent identities in terms of chords.[10]

He may have introduced the law of sines for spherical triangles, though others like Abu-Mahmud Khojandi have been credited with the same achievement:[11]

where are the sides (measured in radians on the unit sphere) and are the opposing angles.[10]

Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi.[10]


Works


He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements.[7]


Legacy



Notes


  1. "بوزجانی". Encyclopaediaislamica.com. Archived from the original on 2008-10-25. Retrieved 2009-08-30.
  2. O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics archive, University of St Andrews
  3. Ben-Menahem, A. (2009). Historical encyclopedia of natural and mathematical sciences (1st ed.). Berlin: Springer. p. 559. ISBN 978-3-540-68831-0. 970 CE Abu al-Wafa al-Buzjani (940–998, Baghdad). Persian astronomer and mathematician.
  4. Sigfried J. de Laet (1994). History of Humanity: From the seventh to the sixteenth century. UNESCO. p. 931. ISBN 978-92-3-102813-7. The science of trigonometry as known today was established by Islamic mathematicians. One of the most important of these was the Persian Abu' l-Wafa' Buzjani (d. 997 or 998), who wrote a work called the Almagest dealing mostly with trigonometry
  5. Subtelny, Maria E. (2007). Timurids in Transition. BRILL. p. 144. ISBN 9789004160316. Persian mathematician Abu al-Wafa Muhammad al-Buzjani
  6. Moussa, Ali (2011). "Mathematical Methods in Abū al-Wafāʾ's Almagest and the Qibla Determinations". Arabic Sciences and Philosophy. Cambridge University Press. 21 (1): 1–56. doi:10.1017/S095742391000007X.
  7. Hashemipour 2007.
  8. Stowasser, Barbara Freyer (2014-05-09). The Day Begins at Sunset: Perceptions of Time in the Islamic World. Bloomsbury Publishing. p. 83. ISBN 978-0-85772-536-3.
  9. Kennedy, E. S. (1956). Survey of Islamic Astronomical Tables. American Philosophical Society. p. 12.
  10. Jacques Sesiano, "Islamic mathematics", p. 157, in Selin, Helaine; D'Ambrosio, Ubiratan, eds. (2000), Mathematics Across Cultures: The History of Non-western Mathematics, Springer, ISBN 1-4020-0260-2
  11. S. Frederick Starr (2015). Lost Enlightenment: Central Asia's Golden Age from the Arab Conquest to Tamerlane. Princeton University Press. p. 177. ISBN 9780691165851.
  12. Youschkevitch 1970.
  13. Raynaud 2012.
  14. Gamwell, Lynn (2 December 2015). "Why the history of maths is also the history of art". The Guardian. Retrieved 3 December 2015.
  15. "Abul Wáfa". Gazetteer of Planetary Nomenclature. USGS Astrogeology Research Program.
  16. D. H. Menzel; M. Minnaert; B. Levin; A. Dollfus; B. Bell (1971). "Report on Lunar Nomenclature by The Working Group of Commission 17 of the IAU". Space Science Reviews. 12 (2): 136. Bibcode:1971SSRv...12..136M. doi:10.1007/BF00171763.
  17. "Abu al-Wafa' al-Buzjani's 1075th Birthday". Google. 10 June 2015.

References





На других языках


[de] Abu l-Wafa

Abu l-Wafa, vollständiger Name arabisch أبو الوفا محمد بن محمد بن يحيى بن إسماعيل بن العباس البوزجاني Abu l-Wafa Muhammad ibn Muhammad ibn Yahya ibn Isma'il ibn al-'Abbas al-Buzdschani, DMG Abū l-Wafā Muḥammad bin Muḥammad bin Yaḥyā bin Ismāʿīl bin al-ʿAbbās al-Būzǧānī, (geboren am 10. Juni 940 in Buzjan, nahe Nischapur in der ostiranischen Region Chorasan; gestorben am 15. Juli 998 in Bagdad) war ein herausragender persischer Mathematiker und Astronom des Mittelalters, welcher mehrere Bücher über angewandte Mathematik schrieb, verschiedene bedeutende trigonometrische Entdeckungen machte und mittlerweile verloren gegangene Kommentare zu den Werken von Euklid, Diophant von Alexandrien und al-Chwarizmi verfasste.
- [en] Abu al-Wafa' Buzjani

[es] Abu'l-Wafa

Abú al-Wafá Buzjani (940-998) fue un matemático y astrónomo persa. Su nombre completo era Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī. Nació el 10 de junio del 940 en Buzhgan (Nishapur, Irán) y murió el 1 de julio de 998 en Bagdad (Irak).[1] A los 19 años de edad se mudó a Irak.

[it] Abu l-Wafa Muhammad al-Buzjani

Abu l-Wafā Muhammad ibn Muhammad ibn Yahya ibn Ismāʿīl al-Būzjānī (in persiano ابوالوفا بوزجانی‎; Baghdad, 940 – Nīshāpūr, 997 o 998) è stato un matematico e astronomo persiano.

[ru] Абу-ль-Вафа аль-Бузджани

Абуль-Вафа Мухаммад ибн Мухаммад аль-Бузджани (араб. ابوالوفا البوزجانی‎, Бузган, 10 июня 940 — Багдад, 998) — персидский учёный X века, один из крупнейших математиков и астрономов средневекового Востока. Учитель Абу-л-Хасана ибн Юниса.



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