English

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

R2 v1 2026-06-21T20:18:42.282Z