Is there a base where pi is a rational number?

No, and this is clear if you know the definition of rational numbers: > A rational number is one which can be expressed as the ratio of two integers. This definition makes no mention of digital representation in any base. read more

Using the same process, you can do this for other numbers. The simplest case is in number base [math]\pi[/math], where [math]\pi = 10[/math]. Nice and simple! A similar principle can be used for "rational" numbers, using rational functions, to find which number base allows a specific fraction to represent pi. read more

I mean sure in base Pi, Pi == 1. I was wondering if there was a number, finite number in like base 1024 or something. read more

One sense in which one can "count" in "base [math]\pi[/math]" is like so: any real number [math]\geq 0[/math] can be written as a Laurent series in [math]\pi[/math], where each coefficient is a natural number [math]<\pi[/math] (non-uniquely in general, but if there is a finite such series, it is unique). read more