Trigonometry

Trigonometry

Al-Biruni was among those who laid the foundation for modern trigonometry. He was a philosopher, geographer, astronomer, physicist and mathematician. Six hundred years before Galgeo, Al-Biruni discussed the theory of the earth rotating about its own axis.

Al-Biruni carried out geodisic measurements and determined the earth's circumference in a most ingenious way. With the aid of mathematics, he enabled the direction of the Qibla to be determined from anywhere in the world.

In the domain of trigonometry, the theory of the functions; sine, cosine, and tangent was developed by Muslim scholars of the tenth century. Muslim scholars worked diligently in the development of plane and spherical trigonometry. The, trigonometry of Muslims is based on Ptolemy's theorem but is superior in two important respects: it employs the sine where Ptolemy used the chord and is in algebraic instead of geometric form.

What is Taught: The Greeks were the developers of trigonometry.
What Should be Taught: Trigonometry remained largely a theoretical science among the Greeks.

It was developed to a level of modern perfection by Muslim scholars, although the weight of the credit must be given to al-Battani.

The words describing the basic functions of this science, sine, cosine and tangent, are all derived from Arabic terms. Thus, original contributions by the Greeks in trigonometry were minimal.

What is Taught: During the 17th century Rene Descartes made the discovery that algebra could be used to solve geometrical problems. By this, he greatly advanced the science of 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, and he was followed by Abu'l Wafa, whose 10th century book utilized algebra to advance geometry into an exact and simplified science.