Abū al-Wafā' Būzjānī
Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (Template:Lang-fa) (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad.
(TO DO: fix math, expand, organize, cross-reference, illustrate.)
Contents
Accomplishments
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.
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.<ref name=MacTutor>Template:MacTutor Biography</ref> 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.<ref name="musa">Template:Cite journal</ref> In Baghdad, he received patronage by members of the Buyid court.Template:Sfn
Astronomy
Abu Al-Wafa' was the first to build a wall quadrant to observe the sky.<ref name=musa /> 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.<ref name="musa" /> 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.
In 997, he participated in an experiment to determine the difference in local time between his location 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.
While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni's.
Almagest
Among his works on astronomy, only the first seven treatises of his Almagest (Kitāb al-Majisṭī) are now extant.
The work covers numerous topics in the fields of plane and spherical trigonometry, planetary theory, and solutions to determine the direction of Qibla.
Mathematics
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.
<math>\sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta</math>
He also discovered the law of sines for spherical triangles:
- <math>\frac{\sin A}{\sin a} = \frac{\sin B}{\sin b}
= \frac{\sin C}{\sin c}</math>
where A, B, C are the sides (measured in radians on the unit sphere) and a, b, c are the opposing angles.<ref name=Sesiano>Jacques Sesiano, "Islamic mathematics", p. 157, in Template:Citation</ref>
Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi.<ref name=Sesiano/>
Works
- Almagest (Template:Lang Kitāb al-Majisṭī).
- A book of zij called Zīj al‐wāḍiḥ (Template:Lang), no longer extant.
- "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (Template:Lang Kitāb fī mā yaḥtāj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).Template:Sfn This text contains over one hundred geometric constructions which have been reviewed and compared with other mathematical treatises. The legacy of this text in Latin Europe is still debated.
- "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", (Template:Lang Kitāb fī mā yaḥtāj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb).
He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements.Template:Sfn
Legacy
The crater Abul Wáfa on the Moon is named after him.
See also
External links
- Abū al-Wafā' Būzjānī @ Wikipedia
