A generalized expression for filling congruent circles in a circle

The paper reports a generalized expression for filling the congruent circles (of radius r) in a circle (of radius R). First, a generalized expression for the biggest circle ® inscribed in the nth part of the bigger circle ® was developed. Further, it was extended as n such circles ® touching each other and the bigger circle ®. To fill the bigger circle ®, the exercise was further repeated by considering the bigger circle radius as R-2r, R-4r and so on. In the process, a generalized expression was deduced for the total no. of such circles ® which could be inscribed in this way of filling the bigger circle ®. The approach does not claim the closest packing always though it could be helpful for practical purposes.