Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae

Authors

Leonhard Euler

Enestrom Number

705

Fuss Index

157

Original Language

Latin

Content Summary

Euler shows that arctan(t) = 1/(1 + t²)∙[1 + 2/3∙t²/(1 + t²) + (2∙4)/(3∙5)∙t²/(1 + t²)² + (2∙4∙6)/(3∙5∙7)∙t²/(1 + t²)³ + ...]. Using this series, and some identities like π = 4∙arctan(1/2) + 4∙arctan(1/3), he calculates π to many decimal places.

Published as

Journal article

Published Date

1798

Written Date

1779

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 11, pp. 133-149.

Opera Omnia Citation

Series 1, Volume 16B, pp. 1-20.

Record Created

2018-09-25