Consider a game with three vertical sticks and 5 circles, where
each circle has a hole in the middle. The circles arranged in
one stick as shown in the picture:
The task is to move all the circles to a nearby stick,
circles can be move from one stick to another, but a
circle cannot be put over a smaller one. What are the
minimum number of steps needed to complete this task?
By definition, a circle is the locus of all points equidistant from a fixed center. However, the circle of Apollonius is defined differently. In the following post I will define and construct an Apollonian circle.