Efficiency of Some Machin-Like Formulas

Machin-like formulas have been used to calculate for a long time. Before 1706, Machin found to 100 places. In 1789, Vega used Hutton's formula to find 140 places (126 correct). In 1841, Rutherford calculated to 208 places (152 correct). In 1844, Dase used Strassnitzky's formula to get 205 places (200 correct). In 1847, Clausen got 250 places (248 correct); he used Machin's and Hutton's formula. In 1853, Rutherford extended his calculation to 440 places (all correct).

Reference

[1] W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 pp. 356–357.

This Demonstration uses some code by Russ Johnson.