I saw recently that you would only need 39 decimals of pi to calculate the diameter of the observable universe to the margin of a single hydrogen atom. So then how in the world do people make the calculations to find more digits of pi? How did we get to so many?
In: Mathematics
Historically, people used the following methods:
1) Measuring
2) Calculating the areas of many-sided polygons, using them as an approximation to a circle
3) Using a number of different formulas that expressed pi as an infinite sum or product, and just kept adding additional terms; for example, the [Leibniz formula](https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80) which is a very simple result that says 1 – 1/3 + 1/5 – 1/7 + 1/9 – … = π/4
We now have 4), an [explicit formula to compute whatever digit of pi you want without having to calculate the preceding digits](https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula)
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