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Home » Solution: Using Ramanujan’s approximation for the circumference of an ellipse: - Upplift

Solution: Using Ramanujan’s approximation for the circumference of an ellipse: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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The square of the sum is $ (4a)^2 = 16a^2 $.
2a^2 + \frac{9d^2}{2} = 16a^2
\Rightarrow \frac{9d^2}{2} = 14a^2
\Rightarrow d^2 = \frac{28a^2}{9}.
The third term is $ a + \frac{d}{2} $, and the first term is $ a - \fr...
\frac{\text{third term}}{\text{first term}} = \frac{a + \frac{d}{2}}{a...
Substitute $ d^2 = \frac{28a^2}{9} \Rightarrow d = a\sqrt{\frac{28}{9}...
\frac{a + \frac{1}{2} \cdot \frac{2a\sqrt{7}}{3}}{a - \frac{3}{2} \cdo...
Multiply numerator and denominator by $ 1 + \sqrt{7} $:
\frac{(3 + \sqrt{7})(1 + \sqrt{7})}{3(1 - 7)} = \frac{3(1) + 3\sqrt{7}...

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