Machin’s formula and Pi. (English) Zbl 1268.65030
Summary: 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 paper closes with an explanation of Takano’s formula.
MSC:
65D20 | Computation of special functions and constants, construction of tables |
11Y60 | Evaluation of number-theoretic constants |