circumference of ellipse

Though, there is no exact formula for circumference of ellipse, like we have for circle, we have an approximate formula which works in most cases.

circumference of ellipse

difficulty in finding exact formula

There is no general formula for the circumference of an ellipse in terms of the semi-major and semi-minor axes of the ellipse that uses only elementary functions. However, there are approximate formulas in terms of these parameters. One such approximation, due to Euler (1773), for the canonical ellipse,

formula for circumference of ellipse

approximate formula for circumference of ellipse

The given formula is the most exact representation of circumference of ellipse till date


An ellipse is described as a curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. Ellipse has two types of axis – Major Axis and Minor Axis. The longest chord of the ellipse is the major axis. The perpendicular chord to the major axis is the minor axis which bisects the major axis at the center.

Given the lengths of minor and major axis of an ellipse, the task is to find the perimeter of the Ellipse.



circumference of ellipse wikipedia

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