Abu al-Wafa' al-Buzjani
Abu al-Wafa' al-Buzjani | |
---|---|
Born | Buzhgan, Iran | 10 June 940
Died | 15 July 998 | (aged 58)
Academic background | |
Influences | Al-Battani |
Academic work | |
Era | Islamic Golden Age |
Main interests | Mathematics and astronomy |
Notable works | Almagest of Abū al-Wafā' |
Notable ideas | |
Influenced | Al-Biruni, Abu Nasr Mansur |
Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (Persian: ابو الوفا بوژگانی, Arabic: ابو الوفا بوزجانی;[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 arithmetic for businessmen contains the first instance of using negative numbers in a medieval Islamic text.
He is also credited with compiling the tables of sines and tangents at 15' intervals. He also introduced the secant and cosecant[broken anchor] 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
[edit]He was born in Buzhgan, (now Torbat-e Jam) in Khorasan (in today's Iran). At age 19, in 959, 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 such as Abu Nasr Mansur, Abu-Mahmud Khojandi, Kushyar Gilani and al-Biruni.[6] In Baghdad, he received patronage from members of the Buyid court.[7]
Astronomy
[edit]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 described a quadrant instrument in his Kitāb az-Zīj.[6] His use of the concept of the tangent helped solve problems involving right-angled spherical triangles. He 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
[edit]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
[edit]He defined the tangent function, and he established several trigonometric identities in their modern form, where the ancient Greek mathematicians had expressed the equivalent identities in terms of chords.[10] The trigonometric identities he introduced were:
He may have developed 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 of the triangle (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
[edit]- Almagest (كتاب المجسطي Kitāb al-Majisṭī).
- A book of zij called Zīj al-wāḍiḥ (زيج الواضح), no longer extant.[7]
- "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (كتاب في ما یحتاج إليه الصانع من الأعمال الهندسية Kitāb fī mā yaḥtāj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).[12] This text contains over one hundred geometric constructions, including for a regular heptagon, which have been reviewed and compared with other mathematical treatises. The legacy of this text in Latin Europe is still debated.[13][14]
- "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", (كتاب في ما يحتاج إليه الكتاب والعمال من علم الحساب Kitāb fī mā yaḥtāj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb).[12] This is the first book where negative numbers have been used in the medieval Islamic texts.[7]
He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements.[7]
Legacy
[edit]- The crater Abul Wáfa on the Moon is named after him.[15][16]
- On 10 June 2015, Google changed its logo in memory of Abu al-Wafa' Buzjani.[17]
Notes
[edit]- ^ "بوزجانی". Encyclopaediaislamica.com. Archived from the original on 25 October 2008. Retrieved 30 August 2009.
- ^ a b c O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics Archive, University of St Andrews
- ^ 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.
- ^ 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
- ^ Subtelny, Maria E. (2007). Timurids in Transition. BRILL. p. 144. ISBN 9789004160316.
Persian mathematician Abu al-Wafa Muhammad al-Buzjani
- ^ a b c d Moussa, Ali (2011). "Mathematical Methods in Abū al-Wafāʾ's Almagest and the Qibla Determinations". Arabic Sciences and Philosophy. 21 (1). Cambridge University Press: 1–56. doi:10.1017/S095742391000007X. S2CID 171015175.
- ^ a b c d e f g h Hashemipour 2007.
- ^ Stowasser, Barbara Freyer (9 May 2014). The Day Begins at Sunset: Perceptions of Time in the Islamic World. Bloomsbury Publishing. p. 83. ISBN 978-0-85772-536-3.
- ^ Kennedy, E. S. (1956). Survey of Islamic Astronomical Tables. American Philosophical Society. p. 12 (134).
- ^ a b c 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
- ^ S. Frederick Starr (2015). Lost Enlightenment: Central Asia's Golden Age from the Arab Conquest to Tamerlane. Princeton University Press. p. 177. ISBN 9780691165851.
- ^ a b Youschkevitch 1970.
- ^ Raynaud 2012.
- ^ Gamwell, Lynn (2 December 2015). "Why the history of maths is also the history of art". The Guardian. Retrieved 3 December 2015.
- ^ "Abul Wáfa". Gazetteer of Planetary Nomenclature. USGS Astrogeology Research Program.
- ^ 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. S2CID 122125855.
- ^ "Abu al-Wafa' al-Buzjani's 1075th Birthday". Google. 10 June 2015.
References
[edit]- O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics Archive, University of St Andrews
- Hashemipour, Behnaz (2007). "Būzjānī: Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā al-Būzjānī". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 188–9. ISBN 978-0-387-31022-0. (PDF version)
- Raynaud, D. (2012), "Abū al-Wafāʾ Latinus? A Study of Method", Historia Mathematica, 39 (1): 34–83, doi:10.1016/j.hm.2011.09.001, S2CID 119600916 (PDF version)
- Youschkevitch, A.P. (1970). "Abū'l-Wafāʾ al-Būzjānī, Muḥammad Ibn Muḥammad Ibn Yaḥyā Ibn Ismāʿīl Ibn al-ʿAbbās". Dictionary of Scientific Biography. Vol. 1. New York: Charles Scribner's Sons. pp. 39–43. ISBN 0-684-10114-9.