The AGM Simple Pendulum
arXiv:1202.2782
Abstract
We present a self-contained development of Gauss' Arithmetic-Geometric Mean (AGM) and the work of A.E. Ingham who obtained rigorous error bounds for the AGM approximations to the period of a simple pendulum
arXiv comment18 pages. Many improvements in exposition in the section on Gauss' proof and on Ingham's computations. A significant expansion in the section on complex multiplication and renormalization