English Title
On various methods for expressing the quadrature of a circle with verging numbers
Enestrom Number
74
Fuss Index
313
Original Language
Latin
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)....
Published as
Journal article
Published Date
1744
Written Date
1738
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
