Is it sensible to consider a base pi number system? Can one make an irrational number rational by defining it as the unit of a counting system? I don't know what constitutes an mathematically consistent 'number line' - this question might not make sense. I'm just thinking that if I use pi as my unit, can write pi as a rational number, since 1 is a rational number. Then I guess most or maybe all other numbers on the number line except integral multiples of pi are irrational?