I agree with you on the absolute beauty of e^{i\pi}+1=0, but I think I would also see a different beauty in e^{ik\pi}=1 for all integer k (if we had \pi=6.28...

I agree with you on the absolute beauty of e^{i\pi}+1=0, but I think I would also see a different beauty in e^{ik\pi}=1 for all integer k (if we had \pi=6.28... instead)