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On last Pi-Day, I’ve sent some friends a poster showing an approximation of \(\pi\) that is individual to them. You can find an example of “my” \(\pi\) here. This time, however, I wanted to calculate the actual Pi as accurate as I could. By hand. Entirely. So I decided to do it up to the 20th decimal place, fairly accurate and the involved numbers will be small enough to fit on printing paper. The method I wanted to use was invented by the great Newton in 1666: \[\pi = 2\, \sum^{\infty}_{k=0}{\...