Coming from a post on theydidthemath talking about Pi, all the top answers begin by explaining that **if** we consider Pi to be a “normal number”, then etc. They also mention we haven’t been able to prove whether it’s a normal number or not yet. What’s that about?
In: Mathematics
A normal number is one where if you took the frequency of each digit occurring, it would form a normal distribution (a bell curve). Basically meaning that it would appear similar to if you rolled a fair die with the same number of faces as the base of the number, you would get a similar distribution. In the case of Arabic numerals that we use, that would be base 10, so a 10 sided die. Note this isn’t saying you would get pi by rolling a 10 sided die over and over, just that the distribution of the frequency of the numbers would be similar, i.e., a normal distribution.
We can’t prove pi is normal or not, because it is infinite, with no repeating pattern. Tests have been done showing that if you calculated pi to hundreds of thousands of digits, it is normal. But pi has only been calculated to trillions of digits (with no repeatable pattern detected), so maybe if it was calculated to trillions of trillions of trillions of digits, it wouldn’t be anymore so it can’t be proven.
For any practical application, you could consider pi as a normal number. But math doesn’t rely on practical applications, it only cares about what can absolutely be proved or disproved, so mathematically, it isn’t determined if pi is normal or not.
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