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 lot of math questions sound very simple when you ask them, but are very hard to prove.
Whether pi is a normal number depends on how many of each digit 0 to 9 you get when you expand it as a decimal. That’s a very simple concept. Except that pi isn’t defined by its decimal expansion, it’s defined as a quantity relating to circles.
Knowing how big pi is doesn’t tell you about all the decimal places, because the farther along you go the less the decimal digits affect how big it is. Calculating any huge number of decimal places doesn’t prove anything because you still don’t know what happens after that. We do know that it doesn’t end in all zeros or any other repeating sequence, but that’s just a consequence of it not being a fraction, and it doesn’t help us make any positive statements about what the digits are.
It’s not even clear how you would go about saying anything meaningful about which digits appear how often in pi. Maybe if you were extremely lucky you could discover one of those infinite sums for pi where the nth term is some coefficient times 10^n or something. I believe there is one for 16^n but even then, if the coefficients are greater than 16 it’s still not strictly the properties of each digit.
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