You have a circle of certain radius $r$.
I want to put a number of points in either of the semicircles. However, no two point can be closer than $r$.
The points can be put anywhere inside the semicircle, on the straight line, inside area, or on the circumference. There is no relation among the points of the two semicircles. But as you can see, eventually they will be the same.
How do I find the maximum number of points that can be put inside the semicircle?