$c$ And $\pi$

$\psi$ is circular  It is wrapped around a circle of perimeter $2\pi r$, where $r$ is the radius from the particle center, travelling at light speed $c$.  On every cycle of period $T=\frac{1}{f}$, it traveled once along the perimeter and has rotated by $2\pi$ rad.  It is then better to redefine light speed with consideration for the value of $\pi$,

$c=\pi*10^8$

instead of

$c=2.99792458*10^8$

such that $r$ is defined/measured without the uncertainty associated with the value of $\pi$.

$\pi$ at light speed will be quite a splat.