How 'Sine' Got Its Name From a Sanskrit Bow-String

If you have ever opened a trigonometry textbook, you have stared at the word sine without realizing it had crossed three civilizations and survived a translation accident to get to you. The function we use today to describe the ratio of a triangle's opposite side to its hypotenuse is named, somewhat absurdly, after a Latin word meaning bay or fold of a garment. The path from a Sanskrit bow-string to the English word sine is a 1,500-year story about scholars copying each other's notes and getting one word wrong.

The Sanskrit origin: jya, the bow-string

The story starts with the 5th-century mathematician Aryabhata, who in 499 CE compiled the Aryabhatiya. In it, he tabulated the lengths of half-chords inside a circle for a given arc. The technical Sanskrit term for this half-chord was ardha-jya (अर्धज्या), literally half bow-string. The word jya (ज्या) means bow-string, and the geometric image is direct: a chord cutting across a circle looks like the strung cord of a bow.

Over time, the abbreviation took over. Sanskrit mathematicians simply used jya on its own, dropping the ardha- prefix. The half-chord became the bow-string. This is the function we would now call sine.

Modern bronze statue of Aryabhata at the Inter-University Centre for Astronomy and Astrophysics, Pune. Image: Wikimedia Commons

The Arabic detour

When Arab scholars began translating Indian mathematical works in the 8th and 9th centuries, they transliterated jya as jiba (جيب) using Arabic letters. The word jiba was not native Arabic. It was just a sound-for-sound copy of the Sanskrit.

Arabic, written without short vowels in most cases, posed a problem. The consonant skeleton j-y-b can be read several ways depending on the vowels you supply. Over generations of copying, readers eventually reinterpreted the foreign-looking jiba as the native Arabic word jaib (جيب), which uses the same consonants and means pocket, fold, or opening of a garment.

This was a misread. The original word was a phonetic borrowing from Sanskrit. But because jaib made sense in Arabic and jiba did not, scholars who had not seen the Sanskrit source eventually thought the geometric function was being called pocket.

The Latin translation

In the 12th century, European scholars began translating Arabic mathematical texts into Latin. Among them was Robert of Chester, who in 1145 translated al-Khwarizmi's algebra into Latin. When Robert and his contemporaries encountered the word jaib, they translated it literally as sinus, the Latin word for bay, fold, or bosom.

This is where the modern term enters European mathematical vocabulary. Sinus became sine in English. The word that originally meant bow-string in Sanskrit, and briefly meant nothing meaningful in Arabic, ended up meaning bay in Latin and from there became the standard term in every trigonometry textbook ever printed.

What this tells us

Three things are worth pulling out of this 1,500-year chain.

First, the technical concept survived intact. The function being described, the half-chord of an arc inside a circle, never changed. What changed was only the name. Mathematical content is largely independent of the language used to discuss it.

Second, the path is asymmetric. Sanskrit to Arabic to Latin moved in one direction, and at each stage a small amount of the original meaning was lost. The bow-string became a pocket, and the pocket became a bay. Each translator was working in good faith, but none of them had access to the source word.

Third, this is not a unique story. The Indian numerals we now call Arabic numerals traveled a similar route. The word algebra comes from the Arabic al-jabr, coined by al-Khwarizmi for the operation of moving terms across an equation. The word algorithm is just al-Khwarizmi Latinized.

Every time you write sin in a notebook, you are writing the last visible trace of a Sanskrit bow-string. The string was strung in the 5th century. We have been pulling it ever since.

Sources

• Aryabhata. Aryabhatiya, c. 499 CE. The original tabulation of half-chords.
• Plofker, Kim. Mathematics in India. Princeton University Press, 2009. The standard modern reference.
• Boyer, Carl B. A History of Mathematics. Wiley, 1991. For the Arabic-to-Latin translation chain.
• Reddit thread on r/sanskrit covering this etymology, March 2026.