Convert a circle to a polygon If I have a circle with a given radius, how calculate I find a regular polygon's vertices, if I know they are all on the circles edge (like in the images below)?


If you are not looking for exactness as an algebraists and merely looking for high precision engineering solution, it is just a matter of looking up the trigonometric table once.
For example, to get the vertices of 11-sided polygon: we need to find 11 equally distant points on the circle of given radius $r$: call the points $P_1,P_2,\ldots, P_{11}$.
$P_1$ will be the point on the positive $x$-axis lying on the circle i.e., $(r,0)$. Then $P_2$ will be the point with co-ordinates $(r\cos \frac{360^\circ}{11}, r\sin \frac{360^\circ}{11})$. Now you know the distance between $P_1$ and $P_2$ use this to mark $P_3$ (that is $P_3$ would be on the circle and at the same distance as $P_1$ is from $P_2$) and so on,
