The Story Of Sine
I’ve been studying mathematics lately and really enjoying it. Here’s an interesting story about the history of the trigonometric function, ‘sine‘.
Early in the 1st millenium A.D., a new way of thinking about chords was coming about. The chord is defined as the straight line that joins two points on the circumference of a circle. The ancient Greeks had developed trigonometric functions to calculate the length of arbitrary chords. But several centuries later, by the early 1st millenium A.D., mathematicians in India began to think about calculating and working with half-chord lengths instead. For this, they developed the familiar ‘sine’ and ‘cosine‘ functions that we still use to this day. The earliest accounts of the use of the half-chord in Indian texts, is from the Surya Siddhanta (c. 300 – 400 AD), written in Sanskrit. The sound of the Sanskrit word used for ‘half-chord’ was ardha-jya [ardha = half, jya = chord]. Perhaps they found this word too long and eventually it was shortened to jya or jiva for all practical purposes.
By roughly the end of the 1st millenium A.D., the vanguard of scientific growth was now in the hands of the Arab world. In translating the works from Sanskrit into Arabic, scholars in the Arab world transliterated and pronounced jiva as jiba [جب]. The sound ‘jiba‘ is recorded in Arabic as two consonants j [ج] and b [ب] with no vowels explicitly written between them. The vowel sounds are merely implied.
Several centuries later, after the decline of scientific growth in the Arab world, came the Europeans. When they in turn came upon the Arabic word for jiva and tried to translate it, they of course ended up with a word, ‘jb‘ [pronounced as ‘jay bee‘]. Apparently, they were oblivious of the implied vowel sounds. Things were dandy for the Arab scientists, but the Europeans couldn’t make any sense of the sound ‘jay bee‘ because such a sound doesn’t exist in any of the words in the Arabic language. They found that the closest sound to ‘jay bee‘, was the sound ‘jaib‘ or ‘ja-eeb‘, in the Arabic word for the mammary gland! And so the Europeans assumed that the half-chord was to be referred to with a Latin word that meant mamma, mammary gland or any of its other synonyms. Perhaps out of modesty, it was ultimately instead decided that the word used for the fold of a cloth utilized to cover a mamma would be appropriate to refer to a half-chord. This word was ‘sinus’. And from this Latin word ‘sinus‘, ultimately came the English word ‘sine‘ that is in use today!
Remarkable, isn’t it?
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