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Almost nobody says Aryabhata — but in 499 CE, he gave a value of π accurate to 4 decimal places, and he even hinted it was irrational. That hint waited 1,100 years for European mathematicians to catch up.
Aryabhatiya, Ganitapada, verse 10. Written in the compact sutra style, where a single line encodes an entire mathematical truth. No working shown. No proof. Just the answer — correct to 4 decimal places, 1,100 years before Europe.
The math is elegant. (100 + 4) × 8 + 62,000 = 62,832. Circumference ÷ Diameter = 62,832 ÷ 20,000 = 3.1416. Modern π = 3.14159265... Aryabhata: 3.14160000... Error: 0.0001%. This is not a coincidence. This is precision engineering of a mathematical constant.
The last word of Aryabhata's verse is "āsannaḥ" — meaning "approaching" or "approximate." He did NOT say "this IS π." He said "this APPROACHES π." This single word implies he knew π could not be expressed exactly as a fraction. The irrationality of π was not proven in Europe until Lambert in 1761. Aryabhata hinted at it in 499 CE.
Madhava of Sangamagrama (~1350 CE, Kerala) derived what Europe calls the "Leibniz formula" for π: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9... He also derived correction terms that dramatically accelerated convergence, computing π to 11 decimal places — a world record that stood for centuries. Leibniz published the same series in 1676 CE, 326 years later. It is now correctly called the Madhava-Leibniz series.
In 1914, Srinivasa Ramanujan published extraordinary formulas for π that converged far faster than anything known. One formula: 1/π = (2√2/9801) Σ [(4n)!(1103+26390n)] / [(n!)⁴ × 396⁴ⁿ]. Each term adds roughly 8 correct decimal digits. It was the basis for William Gosper's 1985 computation of 17 million digits of π. The thread from Aryabhata (499 CE) to Ramanujan (1914 CE) to modern supercomputers is unbroken.
The Sulbasutras (800–200 BCE) — construction manuals for Vedic fire altars — required approximations of π for circular-to-square area conversions. Baudhayana (~800 BCE) used π ≈ 3.088. Apastamba (~600 BCE) improved to 3.0966. Manava (~750 BCE) used 3.16. These are engineering approximations, not mathematical constants — but they show India was computing circles for rituals 1,300 years before Aryabhata.
Every arc-length calculation in Vedic astronomy uses π. The ecliptic (360° circle of the sky) is a circle. Planetary longitudes are arc-measurements. Sine tables — the engine of all Indian astronomy — are based on the unit circle with radius R = 3438 (chosen because 2πR ≈ 21,600 arcminutes = 360°). Without Aryabhata's π, there is no sine table. Without the sine table, there is no Panchang.