Elliptic Integrals of the Second Kind and the Perimeter of the Ellipse

This is the second video in a series of videos on elliptic integrals. The full playlist is available here:    • Elliptic Integrals   Closely related to the elliptic integral of the first kind, which we used in the previous video to express the period of a simple pendulum, is the elliptic integral of the second kind which we use in this video to find the perimeter of the ellipse. This video is really just a kind of warm-up for later questions which we will ask about the ellipse such as: if we would like measure 1/2 of the total arclength in the first quadrant, what can be said about the coordinates of the point at which we must stop along the ellipse? And what angle does the line joining the origin to this point make with the x-axis? (If we were dealing with a circle the answer would be easy: we would just have to halve the amplitude) TIMESTAMPS 0:00 Recap 0:14 Elliptic Integral of Second Kind 0:45 Ellipse (x/a)²+(y/b)²=1 1:34 Parametrization 2:29 Perimeter 4:02 Hypergeometric series for perimeter