# Vega's Calculation of Pi

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In 1776, Hutton derived a formula for . In 1789, Vega used that formula as , to calculate . Vega did not know Machin's formula from 1706, which is better than Hutton's. Vega calculated arctan combining each positive term with the negative term following it. In this way he got two series:

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Contributed by: Izidor Hafner (July 2013)

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Vega sent his paper together with the calculation to *Nova Acta* in 1789.

References

[1] G. Vega, "Détermination de la circonférence d'un cercle," *Nova Acta Academiae Petropolitanae*, IX, 1795, p. 41.

[2] W. W. Rouse Ball and H. S. M. Coxeter, *Mathematical Recreations and Essays*, 13th ed., New York: Dover Publications, 1987 pp. 356–357.

[3] The MacTutor History of Mathematics Archive. "Georg Freiherr von Vega." (Jul 2, 2013) www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Vega.html.

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