Ellipse Circumference (Ramanujan formula)

Description

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. The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1. 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 or transverse diameter. The smaller of these two axes, and the smallest distance across the ellipse, is called the minor axis or conjugate diameter. Ramanujan gives an approximation for the circumference of an ellipse.

Related formulas

Variables

CCircumference of the ellipse (m)
πpi
aThe semi-majior axis (m)
bThe semi-minor axis (m)