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Leibniz' series is just a special case of this series, which was probably the most important series in the history of ?: arctan x = x ? (x3/3) + (x5/5) ? (x7/7) + ? Next, John Machin arrived on the scene. Machin was an English mathematician and professor of astronomy at Gresham College in London...
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Machin was an English mathematician and professor of astronomy at Gresham College in London. Around 1700 he established his important formula: (?/4) = 4 arctan (1/5) ? arctan (1/239). Machin's formula, together with Gregory's series, paved the road for almost every ? thinker from the 18th century until the beginning of the computer era...
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