Trigonometry Was Invented in India:
How "Sine" Is a Sanskrit Word
Every student who has ever written sin(30°) is, without knowing it, using a concept invented in India. The sine function — the foundation of trigonometry — was defined by Āryabhaṭa in 499 CE in his Āryabhaṭīya. And the word "sine" itself traces directly back to the Sanskrit word jyā.
This is not a claim without evidence. The etymology of "sine" is thoroughly documented in the history of mathematics — the word travelled from Sanskrit to Arabic to Latin, picking up a mistranslation along the way. The mathematical concept itself was independently verified by Arab scholars who encountered it through Indian astronomical texts translated into Arabic in the 8th century.
The Word "Sine": A Documented Etymology
jyā (ज्या)
Meaning: "bowstring" — the chord of a circle. Āryabhaṭa used jyā-ardha (half-chord) to define what we now call the sine function. He tabulated the first sine table in the Āryabhaṭīya (499 CE) at 3.75° intervals.
jiba (جيب)
When Arab mathematicians translated Indian astronomical texts in the 8th–9th centuries, they transliterated jyā as jiba — a phonetic approximation. In written Arabic, vowels were omitted, so jiba was written as jb.
sinus
When European scholars translated Arabic mathematical texts in the 12th century (particularly Gherardo of Cremona, c. 1150 CE), they saw jb and mistook it for jaib — the Arabic word for "bay" or "cove." The Latin translation of "bay" is sinus. So "sine" = "bay" = a mistranslation of a transliteration of jyā.
Source: Victor Katz, A History of Mathematics, Addison-Wesley (2009); Kim Plofker, Mathematics in India, Princeton University Press (2009)
Āryabhaṭa's Sine Table (499 CE)
The Āryabhaṭīya gives 24 sine values at 3.75° intervals from 0° to 90° — the world's first trigonometric table. Āryabhaṭa computed these using a recursive difference method: each successive sine value is computed from the previous one using a formula that is essentially the same as what we now call the second-order Taylor expansion of the sine function.
His values are accurate to within 0.1% of modern computed values — extraordinary precision for hand computation in 499 CE, with no calculating tools beyond arithmetic and geometric reasoning.
Source: Āryabhaṭīya, Gaṇita Pāda (Chapter 2), translated by Walter Eugene Clark, University of Chicago Press (1930)
The Kerala School: Infinite Series Before Calculus
Between the 14th and 16th centuries, the Kerala School of Mathematics (Mādhava, Nīlakaṇṭha, Jyeṣṭhadeva) derived infinite series expansions for sine, cosine, and arctangent — the same series attributed in Europe to Gregory (1671), Leibniz (1673), and Newton (1676).
Mādhava's sine series: sin(θ) = θ − θ³/3! + θ⁵/5! − ... was written in Sanskrit verse in the Yuktibhāṣā approximately 200 years before Newton.
Source: K.V. Sarma (ed.), Yuktibhāṣā, Hindustan Book Agency (2008); George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
"The Kerala mathematicians had, in effect, invented calculus before Newton and Leibniz. The evidence is contained in texts that were largely unknown to Western scholars until the 20th century."
— George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
Sources
- • Āryabhaṭīya, translated by Walter Eugene Clark, University of Chicago Press (1930)
- • Victor Katz, A History of Mathematics, Addison-Wesley (2009)
- • Kim Plofker, Mathematics in India, Princeton University Press (2009)
- • George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
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