Abstract:
Elliptic Integrals are of great importance when trying to solve
a wide range of problems. For instance, they can be used to determine
the arc length of an ellipse as well as the position of a pendulum
for large displacements. Calculating elliptic integrals can be
difficult, very often impossible.
A particular type of elliptic integrals can be computed with the
use of the arithmetic-geometric mean, a mixture of the usual
arithmetic and geometric means. First, the integral is expressed
as a series. Gauss used the arithmetic-geometric mean to show that
the series converges. This was considered one of the first serious
discussions of convergent series. In this talk, we will give
the basic definitions and present Gauss' calculations.