So far, it hasn't been proven to be true for any base. For that matter, no irrational algebraic numbers or famous constants have been proven or disproven to normal numbers.
Yes, I knew there was a term for this! I kept looking up things related to "transcendental number" to find the right term for this but I couldn't find one.
lol, I too thought that "transcendental" was the term for this. I was getting quite annoyed that I couldn't find anything in the description about digit statistics.
Kelvin Stott wrote:
But doesn't all this depend on the fact that we just happen to express pi in base 10? What would happen if we expressed pi in base 2
(with "binimals" instead of decimals), or some other base?
Yes, but so far, pi hasn't been shown to be normal in any base. So far it looks normal based on first 30 million digits. Though I suspect that unless pi is specially constructed from the base you're in, it should be normal in all bases right?
How cool would it be if when listening to pi in base 2 you heard a voice or something?
Well, if it is truly a normal number, every conceivable (and probably the ones you can't conceive
) sequence of bits and data will occur at some point in the infinite sequence. In fact, it will occur infinitely often. It's like an infinite number of monkeys typing on and infinite number of typewriters for an infinite period of time. Someone should convert pi to base 27 and see when Shakespear's works start appear