Ramanujan’s approximation for ellipse perimeter (exact for circles).
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How to Use
Enter semi-axes a and b (same units). Circumference is approximate—no closed form exists.
Formula
Ramanujan: h = (a−b)²/(a+b)²; C ≈ π(a+b)[1 + 3h/(10 + √(4−3h))]
FAQ
- Circle case?
- If a = b, you get a circle circumference 2πa.
- Exact formula?
- Ellipse perimeter involves elliptic integrals—this uses a famous approximation.
- Major/minor?
- Semi-axes are half of the corresponding diameters.
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