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| {{Redirect|Abul Wáfa|the lunar crater|Abul Wáfa (crater)}}
| | I am Oscar and I completely dig that title. California is our birth location. The thing she adores most is physique developing and now she is attempting to make money with it. My working day occupation is a meter reader.<br><br>Stop by my web site ... [http://ece.modares.ac.ir/mnl/?q=node/762137 std testing at home] |
| {{Infobox scholar
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| | image = Buzjani, the Persian.jpg
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| | image_size = 200px
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| | name = Abu al-Wafa' al-Buzjani
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| | birth_date = {{Birth date|mf=yes|940|6|10}}
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| | birth_place = [[Buzhgan]]
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| | death_date = 997 or 998 CE
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| | death_place = [[Baghdad]]
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| | era = [[Islamic Golden Age]]
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| | region = [[Baghdad]]
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| | school_tradition =
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| | main_interests = [[Mathematics]] and [[Astronomy]]
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| | notable_ideas = {{Unbulleted list|[[tangent (trigonometry)|Tangent function]]|[[Law of sines]]|Several [[trigonometric identities]]}}
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| | major_works =''Almagest'' of Abū al-Wafā'
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| | influences = [[Al-Battani]]
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| | influenced = [[Al-Biruni]], [[Abu Nasr Mansur]]
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| }}
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| '''Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī''' ({{lang-fa|ابوالوفای بوزجانی}}) <ref>{{cite web|url=http://www.encyclopaediaislamica.com/madkhal2.php?sid=2053 |title=بوزجانی |publisher=Encyclopaediaislamica.com |date= |accessdate=2009-08-30}}</ref> (10 June 940 – 15 July 998) was a [[Persian people|Persian]]<ref>"Iran" in USECO History of Humanity, ed. by M.A. Bakhit, Volume 4 of History of humanity : scientific and cultural development,UNESCO, 2000 pg 375: ""The science of trigonometry as known today was
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| 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
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| mostly with trigonometry"" [http://www.google.com/search?tbm=bks&tbo=1&q=The+science+of+trigonometry+as+known+today+was+established+&btnG=Search+Books#sclient=psy&hl=en&tbo=1&tbm=bks&source=hp&q=The+science+of+trigonometry+as+known+today+was+established+buzjani&aq=f&aqi=&aql=&oq=&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=5565abefa6ad550b&biw=1824&bih=966]</ref> [[Islamic mathematician|mathematician]] and [[Islamic astronomy|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.
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| He is also credited with compiling the tables of sines and tangents at 15' intervals. He also introduced the sec and cosec functions, as well studied the interrelations between the six trigonometric lines associated with an arc.<ref name=MacTutor /> 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.
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| ==Life==
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| He was born in [[Buzhgan]], (now [[Torbat-e Jam]]) in [[Greater Khorasan|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>{{MacTutor Biography|id=Abu'l-Wafa|title=Mohammad Abu'l-Wafa Al-Buzjani}}</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 Mansur|Abu Nasr ibn Iraq]], [[Abu-Mahmud Khojandi]], [[Kushyar ibn Labban]] and [[Al-Biruni]].<ref name="musa">{{cite journal|last=Moussa|first=Ali|title=Mathematical Methods in Abū al-Wafāʾ's Almagest and the Qibla Determinations|journal=Arabic Sciences and Philosophy|year=2011|volume=21|issue=1|publisher=[[Cambridge University Press]]|doi=10.1017/S095742391000007X}}</ref> In Baghdad, he received patronage by members of the [[Buyid]] court.{{sfn|Hashemipour|2007}}
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| ==Astronomy==
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| Abu Al-Wafa' was the first to build a wall [[Quadrant (instrument)|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" />
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| His use of [[tangent (trigonometry)|tangent]] helped to solve problems involving right-angled [[spherical triangle]]s, and developed a new technique to calculate [[sine]] tables, allowing him to construct more accurate tables than his predecessors.{{sfn|Hashemipour|2007}}
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| 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.{{sfn|Hashemipour|2007}} While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni's.{{sfn|Hashemipour|2007}}
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| ===''Almagest''===
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| Among his works on astronomy, only the first seven treatises of his ''Almagest'' (''Kitāb al-Majisṭī'') are now extant.<ref>{{cite book|last=Kennedy|first=E. S.|title=Survey of Islamic Astronomical Tables|year=1956|publisher=American Philosophical Society|page=12}}</ref> The work covers numerous topics in the fields of plane and [[spherical trigonometry]], planetary theory, and solutions to determine the direction of [[Qibla]].<ref name="musa" />{{sfn|Hashemipour|2007}}
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| ==Mathematics==
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| He established several [[trigonometric identity|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.<ref name=Sesiano/>
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| <math>\sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta</math>
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| He also discovered the [[law of sines]] for [[spherical trigonometry|spherical triangle]]s:
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| :<math>\frac{A}{\sin a} = \frac{B}{\sin b}
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| = \frac{C}{\sin c}</math>
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| where ''A'', ''B'', ''C'' are the sides and ''a'', ''b'', ''c'' are the opposing angles.<ref name=Sesiano>Jacques Sesiano, "Islamic mathematics", p. 157, in {{citation|title=Mathematics Across Cultures: The History of Non-western Mathematics|editor1-first=Helaine|editor1-last=Selin|editor1-link=Helaine Selin|editor2-first=Ubiratan|editor2-last=D'Ambrosio|editor2-link=Ubiratan D'Ambrosio|year=2000|publisher=[[Springer Science+Business Media|Springer]]|isbn=1-4020-0260-2}}</ref>
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| Some sources suggest that he introduced the [[tangent (trigonometry)|tangent]] function, although other sources give the credit for this innovation to [[al-Marwazi]].<ref name=Sesiano/>
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| ==Works==
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| * ''Almagest'' (''Kitāb al-Majisṭī'').
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| * A book of [[zij]] called ''Zīj al‐wāḍiḥ'', no longer extant.{{sfn|Hashemipour|2007}}
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| * "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (''Kitāb fī mā yaḥtaj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya'').{{sfn|Youschkevitch|1970}}
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| * "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", (''Kitāb fī mā yaḥtaj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb'').{{sfn|Youschkevitch|1970}} This is the first book where [[negative numbers]] have been used in the medieval Islamic texts.{{sfn|Hashemipour|2007}}
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| He also wrote translations and commentaries on the algebraic works of [[Diophantus]], [[al-Khwārizmī]], and [[Euclid]]'s ''Elements''.{{sfn|Hashemipour|2007}}
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| ==Legacy==
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| The crater [[Abul Wáfa (crater)|Abul Wáfa]] on the Moon is named after him.
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| ==Notes==
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| {{Reflist|close=1}}
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| ==References==
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| * {{MacTutor Biography|id=Abu'l-Wafa|title=Mohammad Abu'l-Wafa Al-Buzjani}}
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| * {{cite encyclopedia | editor = Thomas Hockey et al | last = Hashemipour | first = Behnaz | title=Būzjānī: Abū al‐Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā al‐Būzjānī | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | year = 2007 | location = New York | pages = 188–9 | url=http://islamsci.mcgill.ca/RASI/BEA/Buzjani_BEA.htm | isbn=978-0-387-31022-0| ref=harv}} ([http://islamsci.mcgill.ca/RASI/BEA/Buzjani_BEA.pdf PDF version])
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| * {{cite encyclopedia
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| | last = Youschkevitch
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| | first = A.P.
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| | title = Abū’l-Wafāʾ Al-Būzjānī, Muḥammad Ibn Muḥammad Ibn Yaḥyā Ibn Ismāʿīl Ibn Al-ʿAbbās
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| | encyclopedia = [[Dictionary of Scientific Biography]]
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| | volume = 1
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| | pages = 39–43
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| | publisher = Charles Scribner's Sons
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| | location = New York
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| | year = 1970
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| | isbn = 0-684-10114-9
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| | url = http://www.encyclopedia.com/doc/1G2-2830900031.html
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| | ref=harv
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| }}
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| ==External links==
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| {{Islamic mathematics}}
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| {{Scholars of Khorasan}}
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| {{Authority control|PND=102419213|LCCN=n/89/120201|VIAF=90065177}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Buzjani, Abu Al-Wafa
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| | ALTERNATIVE NAMES = ابوالوفا محمد بن محمد بن یحیی بن اسماعیل بن العباس البوزجانی; Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī
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| | SHORT DESCRIPTION = Persian mathematician and astronomer
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| | DATE OF BIRTH = 940
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| | PLACE OF BIRTH = [[Buzhgan]]
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| | DATE OF DEATH = 15 July 998
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| | PLACE OF DEATH = [[Baghdad]]
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| }}
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| {{DEFAULTSORT:Buzjani, Abu Al-Wafa}}
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| [[Category:Mathematicians of medieval Islam]]
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| [[Category:Astronomers of medieval Islam]]
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| [[Category:10th-century mathematicians]]
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| [[Category:People from Torbat-e Jam]]
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| [[Category:940 births]]
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| [[Category:990s deaths]]
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| [[Category:Iraqi scientists]]
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| [[Category:Iranian scientists]]
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| [[Category:Medieval Persian mathematicians]]
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| [[Category:Medieval Persian astronomers]]
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| [[Category:Medieval Iraqi mathematicians]]
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| [[Category:Medieval Iraqi astronomers]]
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| [[Category:Scientists who worked on Qibla determination]]
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| [[Category:10th-century astronomers]]
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| [[Category:Mathematicians from Nishapur]]
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| [[Category:10th-century Iranian people]]
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| [[Category:Buyid scholars]]
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I am Oscar and I completely dig that title. California is our birth location. The thing she adores most is physique developing and now she is attempting to make money with it. My working day occupation is a meter reader.
Stop by my web site ... std testing at home