Let a circumference $K$ and $200$ points on $K$. Each point is at the end of a diameter corresponding to an integer number of degrees. Prove there are at least two points that are different ends of the same diameter.
There are $200$ points (pigeons $n=200$) and $180$ diameters (holes $m=180)$ :
$200/180 \approx 1.1 \therefore $ by the PHP there will be at least two points that are different ends of the same diameter
Is my proof correct? Is there another formal way to prove it?