When Pi is calculated in decimal you get a never ending remainder. Is this simply a quirk of the decimal system that wouldn’t exist if we were born with 12 fingers instead of 10?
What would happen if your used hexadecimal or unidecimal to find the value of pi. Is there a way to find a theorical base system which would produce a whole number for pi. Like base 42, for example?
In: 15
It can be calculated in any base you want. Irrationality implies that the decimal is non-terminating in *every* base, whereas to be a rational number, there must be some base where the decimal terminates (trivially, when the base is the denominator, though other bases may also terminate).
This goes both ways. If there is a base where a number terminates, that number *must* be rational. If there were a base where pi terminates, pi would necessarily be rational. Since we know pi is irrational, there can be no base where it terminates.
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