yaworsw/euler-manager

---
:id: 199
:name: Iterative Circle Packing
:url: https://projecteuler.net/problem=199
:content: "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.\n\n ![]({{ images_dir }}/p199_circles_in_circles.gif)\n\nAt 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.\n\nWhat fraction of the area is not covered by circles after 10 iterations?
  \ \nGive your answer rounded to eight decimal places using the format x.xxxxxxxx
  .\n\n"