Abū al-Wafā' al-Būzjānī
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Abul Wafa (Persian: ابوالوفا محمد بوژگانی - extended name: Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī) (940 – 997/8) was a Persian mathematician and astronomer. He was born in Buzhgan, Nishapur in Iran.
In 959 AD, he moved to Iraq. He studied mathematics and worked principally in the field of trigonometry. He wrote a number of books, most of which no longer exist. He also studied the movements of the moon. The Abul Wáfa crater on the moon is named for him.
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[edit] Astronomy
He devised a wall quadrant for the accurate astronomy measurement of the declination of stars. He also introduced the tangent function and improved methods of calculating trigonometry tables and developed novel ways of solving some problems of spherical triangles.
[edit] Mathematics
He established the trigonometric identities:
- <math>\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b)</math>
- <math>\cos(2 a) = 1 - 2\sin^2(a)</math>
- <math>\sin(2 a) = 2\sin(a) \cos(a)</math>
and discovered the sine formula for spherical geometry (which looks similar to the law of sines):
- <math>\frac{\sin(A)}{\sin(a)} = \frac{\sin(B)}{\sin(b)} = \frac{\sin(C)}{\sin(c)}</math>
[edit] See also
[edit] Further Reading
- Youschkevitch, A.P. (1970). "Abul Wafa al-Buzjani, Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail Ibn Al-Abbas". Dictionary of Scientific Biography 1. New York: Charles Scribner's Sons. 39-43. ISBN 0684101149.
- O'Connor, John J; Edmund F. Robertson "Mohammad Abu'l-Wafa Al-Buzjani". MacTutor History of Mathematics archive.
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