How are new PI digits discovered?
In: 5
They’re computed. We have exact formula for pi, since as early as Archimedes. Now we have much better formula that are faster to compute with and we have supercomputers.
But you can have a formula for pi without anything fancy. “Knowing” the digits of pi just means being able to approximate pi to certain precision: for example, knowing 6 digits of pi (after the decimal dot) just means knowing that 3.141592 is less than pi, but 3.141593 is more than pi. So a simple way of calculating this is to just find the area of a circle of radius 1, using a grid. If you take a square grid where each cell has very small side length and you count the squares that lie strictly inside the circle you get a lower bound for pi, and if you count the squares that overlap with the circle you get an upper bound of pi. Pick a fine-grained grid (the side length is small) and you will get a good approximation for pi, which gives you the digits.
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