The Forgotten Mathematical Legacy of Aryabhata

Abstract

Aryabhata made pioneering contributions to trigonometry. The sine function finds its first mention in the Aryabhatiya (499 CE), a cryptic work written by Aryabhata when he was 23 years old. The work also indicates how to obtain the difference of sines and cosines by ingenuously using the properties of similar triangles. It then exploits these formulae to obtain the values of the sine function for angles between 0 to 90 degrees. We describe how this was done. In order to make our presentation pedagogical, we take a unit circle and radians instead of the (now) archaic notation in the Aryabhatiya and its commentaries. These seminal contributions of Aryabhata seem forgotten. This is tragic since these methods can be gainfully taught to high and higher secondary school students. We also impress upon the reader the fact that there has been a continuity in the Indian mathematical tradition, starting from the intricate geometric thinking of the Sulbastura in the Vedic era (circa 1000 BCE) to the Calculus of Madhava and his disciples (1350–1600 CE).