# Vega's Second Calculation of Pi

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In 1794 Vega’s second estimate of was published [1]. Vega used Euler’s formula of the form . The picture from [1] ("results from Thesaurus") shows that he calculated to 143 decimal places and the other values to 144 places. In fact he took the calculation of from his first calculation of π, which was correct to 137 decimals.

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Contributed by: Izidor Hafner (August 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In 1789, Vega used the formula , and the sum was not calculated again. We included it in this Demonstration for completeness. The denotations for terms of this sum are from [1–5].

References

[1] J. B. Vega, *Thesaurus Logarithmorum Completus* (logaritmisch-trigonometrischer Tafeln), Leipzig, 1794, p. 633.

[2] J. B. Vega, "Détermination de la démi-circonférence d'un cercle, dont le diamétre est=1," *Nova Acta Academiae Scientiarum Imperialis Petrapolitanea for 1790*, Vol. 9, 1795 pp. 41-44.

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

[4] "Vega Summary." (Aug 6, 2013) www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Vega.html.

[5] I. Hafner, "Vega's Calculation of Pi" from the Wolfram Demonstrations Project—A Wolfram Web Resource. (Jul 10, 2013) demonstrations.wolfram.com/VegasCalculationOfPi.

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