Calculating Pi By Hand - Machin's Method

Here I calculate an approximation of pi by hand using Machin's formula, which I derived in my last video. Around 1706 Machin used this method to calculate pi accurately to 100 places! This would of taken him quite some time to do, and to do so with accuracy would of taken incredible concentration and perseverance. (The great Newton, in 1665 -1666, decades before, using a different method, calculated pi to "just" 16 decimal places). Nowadays we have the benefit of faster converging series such as the Chudnovsky brothers algorithm based off of Ramunujan's pi formula, and use high performance computing to calculate pi in the trillions of digits.

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