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
If pi could be expressed in another number base (let’s call that base b). I.e. pi=x_b/y_b (ratio of two integers in base b), then you could just convert x_b and y_b to base 10 and now have pi as a ratio of two integers in base 10, which we know isn’t possible.
So no, you cannot express pi as a rational number by simply changing bases. Pi is irrational as irrational can be.
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