Inequalities for the perimeter of an ellipse

Abstract

The perimeter of the ellipse x2/a2 + y2/b2 = 1 is 4J (a, b), where J (a, b) is the ‘elliptic integral’This integral is interesting in its own right, quite apart from its application to the ellipse. It is often considered together with the companion integralOf course, we may as well assume that a and b are non-negative.