Saturday, 12 December 2009

The remarkable etymology of sine

(or, How to go from Sanskrit to Latin in four easy steps)

"The ancient Indian mathematician, Aryabhata, had made extensive use of the concept of "sine" (central to modern trigonometry), in the fifth century. He called it jya-ardha, which literally means half-chord in Sanskrit. From there the term moved on in an interesting migratory way, as Howard Eves describes, in his An Introduction to the History of Mathematics (1990, p. 237):
Aryabhata called it ardha-jya ("half-chord") and jya-ardha ("chord-half"), and then abbreviated the term by simply using jya ("chord"). From jya the Arabs phonetically derived jiba, which, following Arabic practice of omitting vowels, was written as jb. Now jiba, aside from its technical significance, is a meaningless word in Arabic. Later writers who came across jb as an abbreviation for the meaningless word jiba substituted jaib instead, which contains the same letters, and is a good Arabic word meaning "cove" or "bay". Still later, Gherardo of Cremona (ca. 1150), when he made his translations from the Arabic, replaced the Arabian jaib by its Latin equivalent, sinus [meaning a cove or a bay], from whence came our present word sine."

[Amartya Sen, Keynote Speech at Beijing Forum 2006]