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Circumference of an ellipse

There are at least several formulas to calculate, or I should better say approximate, the circumference of an ellipse. Although calculating the circumference of a circle is very easy, calculating the circumference of an ellipse is a very difficult task.

Circumference of an ellipse

C ≈ Π × [3 × (R + r) - √ (R + 3 × r)(3 × R + r)]

Where C is circumference, π is 3.14, R is the semi-major axis, and r is semi-minor axis.

The Ramanujan formula that is presented above keeps things simple providing a fair accurate result. For the sake of simplicity I have decided it is the best formula to be known. Other formulas, more accurate, use infinite calculations, factorials, and many other strange Math things.

Example:
If R = 4 and r = 2 then C = ?

C ≈ Π × [3 × (R + r) - √ (R + 3 × r)(3 × R + r)] ≈
≈ 3.14 × [3 × (4 + 2) - √ (4 + 3 × 2)(3 × 4 + 2)] ≈
≈ 3.14 × (18 - √ 140) ≈
≈ 3.14 × (18 - 11.83) ≈
≈ 3.14 × 6.17 ≈ 19.37