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Why isn't there an equal number of blue circles on each side? Why is there an incomplete red circle?

The circles of Apollonius are formed by two pencils: The first is the ratio r of the distances from one point P to two fixed points C and D, denoted as follows: { P{x, y} | dPC / dPD = r } The second is the geometric locus of the P{x, y} that form an inscribed angle theta with the fixed points C and D, it is denoted as follows: { P{x, y} | Angle CPD = theta }.

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The range 0 < r < 1 is mapped on one side and the range 1 < r < Infinity is mapped on the other side of the y axis. You have to use a transformation to get something like a similar distribution of curves on both sides. I used the following, based on the x-intercept p being related to the ratio r by r = -(p-5)/(p + 5) = (5-p)/(5+p) if 0 < p < 5. The code for this adjustment is

{r,Union[
-((Range[9]/2-5)/(Range[9]/2+5)),
{1},
-((Range[9]/2+5)/(Range[9]/2-5))]}

I made some other small adjustments for the sake of performance, which you should feel no need to accept if they interfere with your purpose.

POSTED BY: Michael Rogers

Thank you very much, I will follow your advice, it was sensational, thank you very much!!

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