I have been playing with this idea for a long time... I must warn you I am not proficient at math at all, so I would appreciate answers that I can understand :)
Could we define our math in such a way that
π = 1 ?
If not, why not?
I now see this related question: Is π normal in base π?
I guess this is what I'm thinking about... Just like
2 in binary is
10, we seem to be able to assign numbers to π by choosing a different base. If we would choose base π, π itself would equal 10 right? Could we pick a base such that
π = 1? Would it have advantages? Would it even be possible to use such base, since π is such a weird number?
Also see this question: What would a base $\pi$ number system look like?