# Discoveries in Trigonometry and Geometry

Discoveries in Trigonometry and Geometry

Other significant accomplishments in Trigonometry and Geometry in the Islamic Golden age are listed below. In Trigonometry, we have:

sin(A) sin (B) • Proofs of other trigonometric identities, such as sin(a+b)=sin(a) cos(b)± sin(b)cos(a) and sin(C), and proofs for the spherical and plane sine theorems. (Nasir Al-Din Al-Tusi and Abu Al-Wafa’ Al-Buzjani) a

Telling time by the altitude of the Sun. (by Abu Al-Wafa’ Al-Buzjani)

• Measurements of the radius of the Earth using trigonometry 2. (Abu Rayhan Al-Biruni)

2 Al-Biruni calculate the radius of the earth to be 6339.6 km. The true radius is 6378.1 km.and in Geometry:

• Proof for the general Pythagorean theorem (Thabit ibn Quraa)

• Proof for area of parabola is area of the inscribed triangle (Ibrahim ibn Sinan)

• Constructing an equilateral pentagon in a known square

• Constructing a segment of a sphere equal in volume to one sphere segement and equal in area to a different sphere segment.