Circumference of an Ellipse - Ramanujan, second approximation


An ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve. Ellipses have two mutually perpendicular axes about which the ellipse is symmetric. These axes intersect at the center of the ellipse due to this symmetry. The larger of these two axes, which corresponds to the largest distance between antipodal points on the ellipse, is called the major axis. The smaller of these two axes, and the smallest distance across the ellipse, is called the minor axis.
( A perimeter is a path that surrounds a two-dimensional shape.The perimeter of a circle or ellipse is called its circumference).
The Ramanujan formula calculates the circumference of an ellipse by the lengths of the semi-major axis and the semi-minor axis, using the h component.

Related formulas


CCircumference of an Ellipse (m)
alength of the semi-major axis (m)
blength of the semi-minor axis (m)
h"h component" : (a - b)^2 / (a + b)^2 (dimensionless)