Just throwing a personally unchecked thought out there.

as spheres are kind of efficient, what would maths look like if pi was to equal a whole number in a relative base?

i.e. instead of using decimal, use base 22/3, so that PI becomes 3, and therefore no need to use the word PI

OK I know the numbers become unmanageable without computers, but would that be a more natural base for nature, a nice whole number 3?

If you checked out a few standard formulas, do they become cleaner in this base?

Only a thunk....