The Siddhānta in the Modern World
From Sūrya Siddhānta — The Sun's Treatise of the Heavens, taught by Acharya T Krishnatrey. This lesson is free to read.
<pre data-block="table">Sūrya Siddhānta idea | Chapter | Where it lives today jyā (half-chord) table | 2 | the sine function on every calculator (jyā → sinus) R = 3438 (minutes in a radian) | 2 | the small-angle rule sin θ ≈ θ manda/śīghra epicycles | 2 | the mathematics of planetary position the 12-aṅgula gnomon | 3 | sundials and solar-position geometry parallax (lambana) | 5 | why solar eclipses differ by location nakṣatra coordinates | 8 | star catalogues and celestial coordinates mahī-gola, round earth | 12 | modern geodesy and the shape of the earth four kinds of day/month | 1, 14 | the pañcāṅga and its adhika-māsa leap months sidereal year 365.2587 d | 1 | within ~2 minutes of the modern value</pre> <pre data-block="example">A worked link: the sine table step is 225′ and R = 3438. For the first entry, the arc (225′) and its sine (~224.86′) are nearly equal — exactly what R = 3438 was chosen to make true. The text is using "sin θ ≈ θ for small θ" fifteen centuries before it was written that way.</pre> <pre data-block="research">The descent of "sine" from Sanskrit jyā (via Arabic jyb/jaib → Latin sinus) is standard history of mathematics — see the trigonometry entries in Boyer & Merzbach, A History of Mathematics. Cite that, not folklore.</pre> <pre data-block="quote">Everywhere on the earth-globe people think their own place is on top — but it is a sphere in space: where then is up, where down? — Sūrya Siddhānta 12.53</pre>