Re: [math-fun] Window puzzle, sort of

On 3/12/10, Allan Wechsler <acwacw@gmail.com> wrote:

I have never heard the expression "power of a point" before, so I had to look it up. That's a lovely invariant, that is.

It generalises to a pair of (oriented) circles (or spheres in n-space); depending on how it is normalised, the same bilinear form gives the tangential distance, the incidence angle, or the perpendicular distance from point to line. Followed to its logical conclusion, this leads to (in the plane) tetracyclic coordinates for conformal / inversive / Moebius group geometry, and pentacyclic coordinates for equilong / Laguerre group and contact / Lie-sphere group geometry. Not many people know that ... WFL