#!/usr/bin/env python
# coding=utf-8

"""199. Iterative Circle Packing
https://projecteuler.net/problem=199

Three circles of equal radius are placed inside a larger circle such that each
pair of circles is tangent to one another and the inner circles do not
overlap. There are four uncovered "gaps" which are to be filled iteratively
with more tangent circles.

At each iteration, a maximally sized circle is placed in each gap, which
creates more gaps for the next iteration. After 3 iterations (pictured), there
are 108 gaps and the fraction of the area which is not covered by circles is
0.06790342, rounded to eight decimal places.

What fraction of the area is not covered by circles after 10 iterations?  
Give your answer rounded to eight decimal places using the format x.xxxxxxxx .
"""
