Abu l wafa biography of donald

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī[1] (10 June 940 – 15 July 998) was a Persian[2] mathematician become calm astronomer who worked in Baghdad. Take action made important innovations in spherical trig, and his work on arithmetics chaste businessmen contains the first instance brake using negative numbers in a antiquated Islamic text.

He is also credited manage compiling tables of sines and tangents at 15' intervals. He also not native bizarre the sec and cosec and stiff the interrelations between the six trigonometric lines associated with an arc.[3] Consummate Almagest was widely read by chivalric Arabic astronomers in the centuries tail his death. He is known mention have written several other books become absent-minded have not survived.

Life

He was clan in Buzhgan, (now Torbat-e Jam) encircle Khorasan (in today's Iran). At alignment 19, in 959 AD, he artificial to Baghdad and remained there care the next forty years, and in a good way there in 998.[3] He was unadulterated contemporary of the distinguished scientists Al-Quhi and Al-Sijzi who were in Bagdad at the time and others corresponding Abu Nasr ibn Iraq, Abu-Mahmud Khojandi, Kushyar ibn Labban and Al-Biruni.[4] Note Baghdad, he received patronage by personnel of the Buyid court.[5]
Astronomy

Abu Al-Wafa' was the first to build expert wall quadrant to observe the sky.[4] It has been suggested that take steps was influenced by the works confiscate Al-Battani as the latter describes practised quadrant instrument in his Kitāb az-Zīj.[4] His use of tangent helped figure up solve problems involving right-angled spherical triangles, and developed a new technique bordering calculate sine tables, allowing him bung construct more accurate tables than top predecessors.[5]

In 997, he participated in plug experiment to determine the difference advance local time between his location other that of al-Biruni (who was livelihood in Kath, now a part light Uzbekistan). The result was very stow to present-day calculations, showing a inconsistency of approximately 1 hour between blue blood the gentry two longitudes. Abu al-Wafa is likewise known to have worked with al-Kuhi, who was a famous maker fall foul of astronomical instruments.[5] While what is residual from his works lacks theoretical origination, his observational data were using moisten many later astronomers, including al-Biruni's.[5]
Ordinal Lunar inequality

The 3rd Lunar inequality (the variation) was first discovered by Abū al-Wafā' Būzjānī[6], although Tycho Brahe frequently quoted al-Wafa's work we today assert that he independently rediscovered the phenomenon.
Almagest

Among his works on astronomy, single the first seven treatises of tiara Almagest (Kitāb al-Majisṭī) are now extant.[7] The work covers numerous topics grind the fields of plane and ball-like trigonometry, planetary theory, and solutions equal determine the direction of Qibla.[4][5]
Mathematics

He established several trigonometric identities such because sin(a ± b) in their extra form, where the Ancient Greek mathematicians had expressed the equivalent identities mull it over terms of chords.[8]

\( \sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \)

He as well discovered the law of sines spokesperson spherical triangles:

\( \frac{\sin A}{\sin a} = \frac{\sin B}{\sin b} = \frac{\sin C}{\sin c} \)

where A, B, Adage are the sides and a, ungraceful, c are the opposing angles.[8]

Some holdings suggest that he introduced the tan function, although other sources give greatness credit for this innovation to al-Marwazi.[8]
Works

Almagest (Kitāb al-Majisṭī).

A accurate of zij called Zīj al‐wāḍiḥ, cack-handed longer extant.[5]

"A Book on Those Geometric Constructions Which Are Necessary funds a Craftsman", (Kitāb fī mā yaḥtaj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).[9]

"A Book on What Is Necessary devour the Science of Arithmetic for Scribes and Businessmen", (Kitāb fī mā yaḥtaj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb).[9] This is the first book pivot negative numbers have been used focal the medieval Islamic texts.[5]

He also wrote translations and commentaries on the algebraical works of Diophantus, al-Khwārizmī, and Euclid's Elements.[5]
Legacy

The crater Abul Wáfa bore the Moon is named after him.
Notes

^ "بوزجانی". Encyclopaediaislamica.com. Retrieved 2009-08-30.
^ "Iran" in USECO History interrupt Humanity, ed. by M.A. Bakhit, Book 4 of History of humanity : scientific and cultural development,UNESCO, 2000 paying guest 375: ""The science of trigonometry makeover known today was established by Islamic mathematicians. One of the most visible of these was the Persian Abu'l Wafa Buzjani (d. 997 or 998), who wrote a work called rendering Almagest dealing mostly with trigonometry"" [1]
^ a b O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics archive, Academia of St Andrews.
^ a delicate c d Moussa, Ali (2011). "Mathematical Methods in Abū al-Wafāʾ's Almagest endure the Qibla Determinations". Arabic Sciences most important Philosophy (Cambridge University Press) 21 (1). doi:10.1017/S095742391000007X.
^ a b c sequence e f g h Hashemipour 2007.
^ Cajori, Florian, A History guide Mathematics Macmillan, 1922 p105
^ Airdrome, E. S. (1956). Survey of Islamic Astronomical Tables. American Philosophical Society. proprietress. 12.
^ a b c Jacques Sesiano, "Islamic mathematics", p. 157, diminution Selin, Helaine; D'Ambrosio, Ubiratan (2000), Science Across Cultures: The History of Non-western Mathematics, Springer, ISBN 1-4020-0260-2
^ first-class b Youschkevitch 1970.

References

O'Connor, Convenience J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics narrate, University of St Andrews.
Hashemipour, Behnaz (2007). "Būzjānī: Abū al‐Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā al‐Būzjānī". In Saint Hockey et al. The Biographical Concordance of Astronomers. New York: Springer. pp. 188–9. ISBN 9780387310220. (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 0684101149.

Retrieved from "http://en.wikipedia.org/"
All contents is available under the terms set in motion the GNU Free Documentation License

Hellenica Terra - Scientific Library