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Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail Buzjani (940 – 997 or 998) was a Persian mathematician and astronomer. He was born in Buzhgan, Nishapur in Iran.

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.

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>

In 959 A.D., 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 and there is a crater called Abul Wáfa (crater) on the moon.

[edit] See also

• List of Iranian scientists

[edit] External links

• O'Connor, John J., and Edmund F. Robertson. "Abul Wáfa". MacTutor History of Mathematics archive.ar:أبو الوفا البوزجاني

fa:ابوالوفای بوزجانی fr:Abu l-Wafa id:Abul Wafa Muhammad Al Buzjani it:Abul Wafa Muhammad Al Buzjani nl:Abul Wafa pl:Abu al-Wafa ro:Abul Vefa