eli5: Can’t we just create a different scale with pi as an integer?

Question

We have number like pi and √2 that are problematic in some cases.
Does it exists a branch of math that uses them as units and recalculate every number in that scale to simplify some calculus?

Like
-π, 0,π,2π,3π and so on.

In: 2

Answer 1

We like our scale because we can count 1, 2, 3 on our fingers. And there’s a one-to-one correspondence between our fingers and the apples we’re counting. 3 fingers = 3 apples. I’ll let others opine about having a second scale as you suggest.