Ellipse
Estimates ellipse perimeter and area from semi-axes a and b (area S = πab).
Area
6,28
Perimeter
9,69
Perimeter is Ramanujan’s approximation π[3(a+b)−√((3a+b)(a+3b))], not an exact elliptic integral.
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Formula
A = πab; C ≈ π[3(a+b) − √((3a+b)(a+3b))] (Ramanujan approximation)
Example: a = 2, b = 1 → A = 2π ≈ 6.28
Methodology
Area S = π × a × b from semi-axes a and b. Perimeter uses Ramanujan approximation.
Example
Semi-axes 5 and 3 cm: S ≈ 47.12 cm².