Abu al-Wafa' Buzjani
Abu al-Wafa' al-Buzjani | |
---|---|
Born | Buzhgan, Iran | June 10, 940
Died | July 15, 998 Baghdad | (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: ابوالوفا بوزجانی or بوژگانی)[1] (10 June 940 – 15 July 998)[2] was a Persian[3][4] 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.
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 for the next forty years, and died there 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 ibn Iraq, Abu-Mahmud Khojandi, Kushyar ibn Labban and Al-Biruni.[5] In Baghdad, he received patronage by members of the Buyid court.[6]
Astronomy[]
Abu Al-Wafa' was the first to build a wall quadrant to observe the sky.[5] 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.[5] 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.[6]
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). 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.[6] While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni.[6]
Almagest[]
Among his works on astronomy, only the first seven treatises of his Almagest (Kitāb al-Majisṭī) are now extant.[7] The work covers numerous topics in the fields of plane and spherical trigonometry, planetary theory, and solutions to determine the direction of Qibla.[5][6]
Mathematics[]
He defined the tangent function, and he established several trigonometric identities such as sin(a ± b) in their modern form, where the Ancient Greek mathematicians had expressed the equivalent identities in terms of chords.[8]
He also discovered the law of sines for spherical triangles:
where A, B, C are the sides (measured in radians on the unit sphere) and a, b, c are the opposing angles.[8]
Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi.[8]
Works[]
- Almagest (كتاب المجسطي Kitāb al-Majisṭī).
- A book of zij called Zīj al‐wāḍiḥ (زيج الواضح), no longer extant.[6]
- "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).[9] 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.[10][11]
- "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).[9] This is the first book where negative numbers have been used in the medieval Islamic texts.[6]
He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements.[6]
Legacy[]
- The crater Abul Wáfa on the Moon is named after him.[12][13]
- On 10 June 2015, Google changed its logo in memory of Abu al-Wafa' Buzjani.[14]
Notes[]
- ^ "بوزجانی". Encyclopaediaislamica.com. Archived from the original on 2008-10-25. Retrieved 2009-08-30.
- ^ Jump up to: 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
- ^ Jump up to: a b c d 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.
- ^ Jump up to: a b c d e f g h Hashemipour 2007.
- ^ Kennedy, E. S. (1956). Survey of Islamic Astronomical Tables. American Philosophical Society. p. 12.
- ^ Jump up to: 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
- ^ Jump up to: 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.
- ^ "Abu al-Wafa' al-Buzjani's 1075th Birthday". Google. 10 June 2015.
References[]
- 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 (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. 1. New York: Charles Scribner's Sons. pp. 39–43. ISBN 0-684-10114-9.
External links[]
- Mathematicians of medieval Islam
- Astronomers of medieval Islam
- 10th-century Persian mathematicians
- People from Torbat-e Jam
- 940 births
- 998 deaths
- Medieval Persian astronomers
- Scientists who worked on qibla determination
- 10th-century astronomers
- Mathematicians from Nishapur
- 10th-century Iranian people
- Buyid scholars