Machin-like formulae
M000000457: Hermann's formula
$$\pi=8\arctan\left(\frac{1}{2}\right)-4\arctan\left(\frac{1}{7}\right)$$
Name
Hermann's formula
Compact formula
8[2] - 4[7]
Lehmer's measure
4.50522
References
Hermann, Jakob. Letter to Gottfried Leibniz, 1706. [Published in 1849 in
Leibnizens mathematische schriften
, pages 302-304.]
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