English Title

Annotations to a certain passage of Descartes for finding the quadrature of the circle

Authors

Leonhard Euler

Enestrom Number

275

Fuss Index

315

Original Language

Latin

Published as

Journal article

Published Date

1763

Written Date

1758

Archive Notes

According to Jacobi, a treatise with this title was read to the Berlin Academy on July 20, 1758. According to St. Petersburg Academy records, it was presented to that Academy on October 15, 1759.

Content Summary

Euler shows that 4π = tan(π /4) + 1/2∙tan(pi/8) + 1/4∙tan(π /16) + 1/8∙tan(π /32) + …. Combining this with the integral of arctangent, he gets an expression for π /4 that converges rapidly. For n=5, it gives 12 decimal places of accuracy.

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 157-168.

Opera Omnia Citation

Series 1, Volume 15, pp.1-15.

Record Created

2018-09-25

Included in

Mathematics Commons

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