system of equations / apollonian gasket



Adam Majewski wrote:

>eq12: (x1-x2)^2 + (y1 -y2)^2 - (r1-r2)^2;

I think you mean (r1+r2)^2 here and in the other two equations.  In fact, you don't really need eq12.  You can solve it like this:

eq13:(x1-x3)^2+(y1-y3)^2-(r1+r3)^2;
eq23:(x2-x3)^2+(y2-y3)^2-(r2+r3)^2;
solve([eq13,eq23],[x3,y3]);

Maxima returns:

[[x3=0,y3=50-50*sqrt(3)],[x3=0,y3=50*sqrt(3)+50]]

These represent, of course, the two possible tangent circles (above and below).

Ed