Trigonometry

Trigonometry

Published: 2002

Al-Biruni helped lay the foundation for modern Trigonometry. He was a philosopher, geographer, astronomer, physicist, and mathematician. Six hundred years before Galileo, Al-Biruni discussed the theory that the Earth rotates on its axis. Al-Biruni carried out geodesic measurements and determined the earth’s circumference most ingeniously.

Using mathematics, he enabled people to determine the Qibla direction from anywhere in the world. In trigonometry, 10th-century Muslim scholars developed the functions sine, cosine, and tangent. Muslim scholars worked diligently to develop plane and spherical trigonometry.

Muslim trigonometry is based on Ptolemy’s theorem but is superior in two important respects: it uses the sine where Ptolemy used the chord, and it is algebraic rather than geometric.

What is Taught:
The Greeks developed trigonometry.

What Should be Taught:
The Greeks kept trigonometry largely theoretical.
Muslim scholars developed it to a level of modern perfection, though al-Battani deserves credit.
The terms describing this science’s basic functions, sine, cosine, and tangent, are all derived from Arabic. Thus, the Greeks’ original contributions to trigonometry were minimal.

What is Taught:
In the 17th century, René Descartes discovered that Algebra could solve geometrical problems. This greatly advanced geometry.

What Should be Taught:
Mathematicians of the Islamic Empire accomplished precisely this as early as the 9th century A.D. Thabit bin Qurrah was the first to do so. Abu’l Wafa followed, and his 10th-century book used algebra to make geometry an exact, simplified science.

The renaissance of astronomy in Baghdad in the 9th and 10th centuries. Al-Bīrūnī — Different phases of the moon- al-Biruni