The Nineteenth Byte

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Peter Taylor

22:00

@xnor Finding one root of a quadratic given the other by use of either of the symmetric polynomials. What we have here is an infinite descent through a hierarchy of circles.

Martin Büttner

@PeterTaylor But couldn't I do that anyway, once I've found the 4th circle GPS-style?

Peter Taylor

But if you've got that code already, why would you not use it at all levels of the hierarchy? The fourth circle is necessary to make the approach a reasonable golf contender.

Martin Büttner

hmm, I see

Well one reason to use it is that you could save the check for which solution you already have at each step.

but that might be too little to make the alternative approach worthwhile

Peter Taylor

22:22

The other reason would be to get the centre as well as the radius. artofproblemsolving.com/blog/34543 is the main idea; the circumcentre has nice barycentrics, and the circumradius has a relatively nice expression in terms of the circle radii: mathworld.wolfram.com/Circumradius.html#eqn11

Martin Büttner

The only problem I have with that is that the input to the programs needs to be very specific. That is, to test the program you need to figure out valid circle quadruplets that are tangent to begin with.

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