جيب

The word sine hides one of history's most consequential translation accidents. The Indian mathematician Aryabhata in the 5th century CE developed the concept of the half-chord of a circle arc, which he called jya-ardha (half-chord) or simply jya in Sanskrit. Arab mathematicians translating Indian astronomical texts in the 8th–9th centuries rendered jya phonetically as jiba (جيبا) — a meaningless transcription. When later Arab mathematicians worked with this text, they misread the abbreviation jiba as jayb (جيب), a real Arabic word meaning 'bosom,' 'pocket,' or 'fold of a garment.'

When the 12th-century European scholar Robert of Chester translated Arabic mathematical texts into Latin at Toledo, he encountered jayb (bosom) and translated it literally into Latin as sinus — which also means 'fold,' 'curve,' 'bay,' or 'bosom' in Latin. This translation was accurate in that it correctly rendered the Arabic word Robert saw; the problem was that the Arabic was itself a misreading of a phonetic transcription of a Sanskrit mathematical term. The sine function's name is therefore: a Sanskrit mathematical concept, phonetically transcribed into Arabic, misread as an Arabic word meaning bosom, then translated into the Latin word for the same anatomical region.

Despite — or perhaps because of — this etymology, the Latin sinus, shortened to sine (abbreviation: sin), became the standard term for one of the six fundamental trigonometric functions. The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Sine functions describe wave motion, circular motion, oscillation, and countless other periodic phenomena. The 16th-century European development of trigonometry as a distinct mathematical discipline codified sine alongside cosine, tangent, and the other functions, building on both the Indian original and the Arabic transmission.

Today sine is one of the most used functions in mathematics, physics, engineering, and signal processing. Sine waves describe sound, light, alternating current, ocean waves, and the vibration of every string instrument. The sin button appears on every scientific calculator and on every phone. The mistranslated bosom-word from medieval Toledo is now fundamental to every field of science and engineering that deals with periodic phenomena — which is nearly all of them.