Abul Wáfa
Encyclopedia
Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī (10 June 940 – 15 July 998) was a Persian
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 of compiling tables of sines and tangents at 15' intervals. He also introduced the sec and cosec and 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.
, (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. He was a contemporary of the distinguished scientists Al-Quhi 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
. In Baghdad, he received patronage by members of the Buyid court.
to observe the sky. 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.
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 al-Kuhi, who was a famous maker of astronomical instruments. While what is extant from his works lacks theoretical innovation, his observational data were using by many later astronomers, including al-Biruni's.
, planetary theory, and solutions to determine the direction of Qibla
.
mathematicians had expressed the equivalent identities in terms of chords.
He also discovered the law of sines
for spherical triangle
s:
where A, B, C are the sides and a, b, c are the opposing angles.
Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi
.
He also wrote translations and commentaries on the algebraic works of Diophantus
, al-Khwārizmī, and Euclid
's Elements.
Persian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...
mathematician and astronomer
Islamic astronomy
Islamic astronomy or Arabic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age , and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and...
who worked in Baghdad. He made important innovations in spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text.
He is also credited of compiling tables of sines and tangents at 15' intervals. He also introduced the sec and cosec and 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 BuzhganBuzhgan
Būzhgān is a village in Torbat-e-Jam County in Iran's Khorasan-e Razavi province. Historically Buzhgan was a city and was the seat of government in the historic Persian province of Jam ....
, (now Torbat-e Jam) in Khorasan
Greater Khorasan
Greater Khorasan or Ancient Khorasan is a historical region of Greater Iran mentioned in sources from Sassanid and Islamic eras which "frequently" had a denotation wider than current three provinces of Khorasan in Iran...
(in today's Iran). At age 19, in 959 AD, he moved to Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...
and remained there for the next forty years, and died there in 998. He was a contemporary of the distinguished scientists Al-Quhi and Al-Sijzi
Al-Sijzi
Abu Sa'id Ahmed ibn Mohammed ibn Abd Jalil Sijzi was a Persian astronomer and mathematician from Sistan, a region lying in the south-west of Afghanistan and south-east of Iran....
who were in Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...
at the time and others like Abu Nasr ibn Iraq
Abu Nasr Mansur
Abu Nasr Mansur ibn Ali ibn Iraq was a Persian Muslim mathematician. He is well known for his work with the spherical sine law....
, Abu-Mahmud Khojandi, Kushyar ibn Labban
Kushyar ibn Labban
Abul-Hasan Kūshyār ibn Labbān ibn Bashahri Gilani , also known as Kūshyār Gīlānī , was a Persian mathematician, geographer, and astronomer from Gilan, south of the Caspian Sea, Iran....
and Al-Biruni
Al-Biruni
Abū al-Rayḥān Muḥammad ibn Aḥmad al-BīrūnīArabic spelling. . The intermediate form Abū Rayḥān al-Bīrūnī is often used in academic literature...
. In Baghdad, he received patronage by members of the Buyid court.
Astronomy
Abu Al-Wafa' was the first to build a wall quadrantQuadrant (instrument)
A quadrant is an instrument that is used to measure angles up to 90°. It was originally proposed by Ptolemy as a better kind of astrolabe. Several different variations of the instrument were later produced by medieval Muslim astronomers.-Types of quadrants:...
to observe the sky. It has been suggested that he was influenced by the works of Al-Battani
Al-Battani
Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī al-Ṣābiʾ al-Battānī was a Muslim astronomer, astrologer, and mathematician...
as the latter describes a quadrant instrument in his Kitāb az-Zīj.
His use of tangent helped to solve problems involving right-angled spherical triangles, and developed a new technique to calculate sine
Sine
In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
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
Uzbekistan
Uzbekistan , officially the Republic of Uzbekistan is a doubly landlocked country in Central Asia and one of the six independent Turkic states. It shares borders with Kazakhstan to the west and to the north, Kyrgyzstan and Tajikistan to the east, and Afghanistan and Turkmenistan to the south....
). 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 al-Kuhi, who was a famous maker of astronomical instruments. While what is extant from his works lacks theoretical innovation, his observational data were using 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 trigonometrySpherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
, planetary theory, and solutions to determine the direction of Qibla
Qibla
The Qiblah , also transliterated as Qibla, Kiblah or Kibla, is the direction that should be faced when a Muslim prays during salah...
.
Mathematics
He established several trigonometric identities such as sin(a ± b) in their modern form, where the Ancient GreekAncient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
mathematicians had expressed the equivalent identities in terms of chords.
He also discovered the law of sines
Law of sines
In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles...
for spherical triangle
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
s:
where A, B, C are the sides and a, b, c are the opposing angles.
Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi
Al-Marwazi
Ahmad ibn 'Abdallah Habash Hasib Marwazi was an astronomer, geographer, and mathematician from Merv in Khorasan.He flourished in Baghdad, and died a centenarian after 869...
.
Works
- Almagest (Kitāb al-Majisṭī).
- A book of zijZijZīj is the generic name applied to Islamic astronomical books that tabulate parameters used for astronomical calculations of the positions of the Sun, Moon, stars, and planets. The name is derived from the Middle Persian term zih or zīg, meaning cord...
called Zīj al‐wāḍiḥ, no longer extant.
- "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (Kitāb fī mā yaḥtaj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).
- "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). This is the first book where negative numbers have been used in the medieval Islamic texts.
He also wrote translations and commentaries on the algebraic works of Diophantus
Diophantus
Diophantus of Alexandria , sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost...
, al-Khwārizmī, and Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
's Elements.