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# Abul Wefa *(Abu'l Wafa, Albuzdschani)*

Died: 998 AD, at 58 years of age.

Nationality: Persian

Categories: Astronomers, Mathematicians

940 - Abul Wafa was born in Buzjan, Nishapur.

959 - He learned mathematics in Baghdad and migrated to Iraq. Abul Wafa helped in bringing about a lot of theories in several branches of mathematics, particularly geometry and trigonometry. In geometry his contribution lies in solving geometrical problems with opening of the compass; construction of a square equivalent to other squares; regular polyhedral; construction of regular hexagon taking for its side half the side of the equilateral triangle inscribed in the same circle; constructions of parabola by points and geometrical solution of the equations: "x4 = a and x4 + ax3 = b". Abul Wafa's contribution to the development of trigonometry was extensive. He was the first to show the generality of the sine theorem relative to spherical triangles. He developed a new method of constructing sine tables, the value of sin 30' being correct to the eighth decimal place. He also developed relations for sine (a+b) and the formula: "2 sin2 (a/2) = 1 - cos a, and sin a = 2 sin (a/2) cos (a/2)". 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.

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