Mathematics

T1

A garden pond shaped like an ellipse — longer diameter L, shorter diameter S. How much area does it cover? In 850 CE, Mahāvīra's answer: take S/4, multiply by 2L+S. The formula is approximate — it uses the Indian rounding of π as 3 — but recovers the modern π·a·b correctly for circular limits and stays within ~10% for moderate eccentricities. Indian mensuration teachers kept teaching it for the next thousand years. The first explicit ellipse-area formula in surviving Sanskrit mathematics.

From the source

One-fourth of the (shorter) diameter, multiplied by the circumference, gives rise to the (measure of the) area (thereof).
The Ganita-sara-sangraha of Mahaviracarya, 850ch7.v21.dup1
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