English Title
Annotations to a certain passage of Descartes for finding the quadrature of the circle
Enestrom Number
275
Fuss Index
315
Original Language
Latin
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 tan(π/4) + 1/2∙tan(π/8) + 1/4∙tan(π/16) + 1/8∙tan(π/32) + … = 4π. Combining this with the integral of arctangent, he obtains an expression for π/4 that converges rapidly. For n=5, it gives 12 decimal places of accuracy.
Published as
Journal article
Published Date
1763
Written Date
1758
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
