Mathematicians Of The Day

6th July



On this day in 1708, de Moivre wrote to Johann Bernoulli about Machin's series: (1654239)13(165342393)...=3.14159...=π(\frac{16}{5} - \frac{4}{239}) - \frac{1}{3} (\frac{16}{5^3} - \frac{4}{239^3})\, ... = 3.14159 ... = \pi, on this occasion giving two different proofs that it converges to π.
This series follows from the identity π4=4tan115tan11239\frac {\pi }{4}=4\tan^{-1} {\frac {1}{5}}-\tan^{-1} {\frac {1}{239}}.

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Quotation of the day

From Ronald Graham
Well, as you know, there are 24 hours in every day. And if that's not enough, you've always got the nights!