Very novice amateur mathematician here. My daughter (8 yo) is a math junkie and is trying to wrap her head around irrational numbers. We were talking about $\pi$, and I rambled on about how folks have put a lot of energy into researching the 'following digits' of $\pi$ and their properties. 

Then it occurred to me that we usually discuss $\pi$ in Base 10, simply because humans have 10 fingers and toes, etc. Would any properties ascribed to qualities of digits of $\pi$ vanish in other bases / (base 2, 12, etc.) 

Please forgive my naivety...