The word sine began as Aryabhata's 'half-chord' and a translator's mix-up
Aryabhata called the sine ardha-jya, half-chord. Arabic translators wrote it jiba, which without vowels became jb, then was misread as jaib, a fold in a garment. In the 12th century Gherardo of Cremona rendered that as Latin sinus, meaning a bay, and English inherited sine.
Aryabhata, who lived from 476 to 550 CE, was the first of the great mathematician-astronomers of classical India. His birth year comes from his own remark that he was 23 in the year 3600 of the Kali Yuga, which is 499 CE. He called himself a native of Kusumapura, identified with Pataliputra near modern Patna, and a verse says he headed an institution there. Claims that he led Nalanda university remain speculation. His name is properly Aryabhata, not Aryabhatta: Brahmagupta spells it that way in more than a hundred places, and the longer form would usually break the metre.
Only one of his works survives, the Aryabhatiya, a compact text of 108 verses plus 13 introductory ones, each line serving as a memory aid that later commentators unpacked. It covers arithmetic, algebra and both plane and spherical trigonometry, including a table of sines packed into a single verse, with numbers encoded as letters of the alphabet in the old Sanskrit manner. He used a place-value system without a zero symbol, though some historians argue zero is implicit in it. A second treatise, the Arya-siddhanta, is lost but known through Varahamihira and others, and described instruments such as a gnomon and water clocks.
His rule for the circumference of a circle 20,000 units across is accurate to about two parts in a million. He called the result āsanna, approaching, which some read as a hint that pi is irrational, a fact Europe proved only in 1761 through Lambert. The approximation later appeared in Al-Khwarizmi's algebra after an Arabic translation around 820. He also gave formulas for sums of squares and cubes and a recursive technique, kuttaka, meaning pulverizing, for whole-number solutions of equations of the form ax plus by equals c; it became so central that early Indian algebra was named after it.
In astronomy he explained the westward drift of the stars with an image of a man in a moving boat who sees the fixed shore sliding backward. His commentators kept the work alive for centuries, from his disciple Bhaskara I around 600 CE to Nilakantha Somayaji in 1465.
Source: Aryabhata
