The AGM Simple Pendulum
Classical Analysis and ODEs
2014-09-02 v2
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
Cite
@article{arxiv.1202.2782,
title = {The AGM Simple Pendulum},
author = {Mark B. Villarino},
journal= {arXiv preprint arXiv:1202.2782},
year = {2014}
}
Comments
18 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