English Title

On various methods for expressing the quadrature of a circle with verging numbers

Authors

Leonhard Euler

Enestrom Number

74

Fuss Index

313

Original Language

Latin

Published as

Journal article

Published Date

1744

Written Date

1738

Content Summary

In this paper, adjacent to E72, Euler studies methods for approximating π. He presents various clever ways to decompose arctan(1) = π/4 as the sum of terms of the form arctan(1/n), then suggests using the Leibniz series to get a good approximation for π. He also introduces a way to calculate the number of terms necessary to produce an approximation accurate to a given number of decimals. He closes the paper with the "not inelegant" theorem that sin(x)/x = cos(x/2)∙cos(x/4)∙cos(x/8)∙cos(x/16)....

Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 9, pp. 222-236.

Opera Omnia Citation

Series 1, Volume 14, pp.245-259.

Record Created

2018-09-25

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