Approximations for the period of the simple pendulum based on the arithmetic-geometric mean

Approximations for the period of the simple pendulum based on the arithmetic-geometric mean

We use the arithmetic-geometric mean to derive approximate solutions for the period of the simple pendulum. The fast convergence of the arithmetic-geometric mean yields accurate solutions. We also discuss the invention of the pendulum clock by Christiaan Huygens in 1656–1657.

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Veröffentlicht in:American journal of physics 2008-12, Vol.76 (12), p.1150-1154
Hauptverfasser: Carvalhaes, Claudio G., Suppes, Patrick
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Geometry
Mathematics
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Zusammenfassung:We use the arithmetic-geometric mean to derive approximate solutions for the period of the simple pendulum. The fast convergence of the arithmetic-geometric mean yields accurate solutions. We also discuss the invention of the pendulum clock by Christiaan Huygens in 1656–1657.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.2968864