Born : June 10, 940 Buzhgan, Iran
Died : July 15, 998 (aged 58) Baghdad
Main : Mathematics and Astronomy.
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) (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
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. 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. In Baghdad, he received patronage by
members of the Buyid court.
Astronomy
Abu Al-Wafa' was the
first to build a wall quadrant 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 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.
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.
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.
Some sources suggest
that he introduced the tangent function, although other sources give
the credit for this innovation to al-Marwazi.
Sumber
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