The circle packing in a circle can be found in https://en.wikipedia.org/wiki/Circle_packing_in_a_circle http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html
As the number of little circles (packing 1 big circle) goes to inf, how to prove that the density (area of little circles/area of big circle) goes to 1?
This is not trivial without proving it because any of the gaps between the little circles will be multiplied by a number proportional to the number of the little circles, which is a huge number.