# Reconstruction of Vega's First Calculation of Pi

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In 1789, Vega sent his first calculation of to the Petersburg Academy. He used the formula , where is the smaller part and is the larger part. Vega calculated arctan by 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 (November 2013)

Open content licensed under CC BY-NC-SA

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References

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

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

[3] The MacTutor History of Mathematics Archive. "Georg Freiherr von Vega." (Jan, 2012) www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Vega.html.

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