The AGM Simple Pendulum
Mark B. Villarino
TL;DR
This paper provides a comprehensive explanation of Gauss' AGM method and discusses Ingham's work on establishing rigorous error bounds for AGM approximations of the simple pendulum's period.
Contribution
It introduces a self-contained development of AGM and incorporates Ingham's rigorous error bounds, enhancing the understanding of pendulum period approximations.
Findings
Derived precise error bounds for AGM approximations
Demonstrated the effectiveness of AGM in pendulum period calculations
Provided a clear, self-contained presentation of AGM theory
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
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Scientific Research and Discoveries · Engineering Education and Pedagogy