How are new PI digits discovered?
In: 5
While we can’t cleanly express the value of Pi, we can express an infinite series that converges to Pi.
An infinite series is just a continuous sum of smaller and smaller terms. Eventually the terms being added are so small that we can be certain of the values of the higher digits.
For example, we know that Pi/4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11… and so on. If you decide to cut off that formula at some point, you can just run the calculations and figure out an approximate value. The larger more terms you have, the more precise you are. There’s a secondary calculation you can do that shows how many digits you can trust from your original answer (i.e., how big the portion you chopped off was).
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