Authors

Leonhard Euler

Enestrom Number

705

Fuss Index

157

Original Language

Latin

Published as

Journal article

Published Date

1798

Written Date

1779

Content Summary

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

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

Included in

Mathematics Commons

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