IJPAM: Volume 82, No. 3 (2013)
MACHIN'S FORMULA AND PI
Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN
Abstract. This article explains the calculation of Pi historically, focusing on Machin's formula. Archimedes' formula is shown first, followed by Machin's formula using Gregory's formula. Machin's formula makes particularly ingenious use of the double and quadruple angle trigonometric addition formulae. The chapter closes with an explanation of Takano's formula.
Received: September 25, 2012
AMS Subject Classification: 68N02, 00A09, 97A20
Key Words and Phrases: Pi, Machin's formula, Archimedes' method, Gregory's formula, Pythagorean triangles, Takano's formula
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 3
