Hi Bill: These look extremely interesting. However, I'm not a Mathematica fan or user. Any chance of showing this in Maxima? BTW, I haven't worked on the complex # stuff for triangle centers for a couple of years, but I still believe that "there's gold in them thar hills" ! In particular, I think that there are complex & quaternion formulae that are analogs of existing scalar formulae. I.e., the scalar formula may be the *absolute value* of the complex and/or quanternion formula. At 02:14 PM 1/28/2016, Bill Gosper wrote:
I hope Henry or someone is collecting our various complex number geometricks e.g., PolygonArea[L_List] := Total[MapThread[Im[#1\[Conjugate]*#2] &, {L, RotateLeft[L]}]]/2
line segment intersect Interseg[z1_, z2_, z3_, z4_] := Block[{z12 = z1 - z2, z34 = z3 - z4}, (z34*Im[z2*z1\[Conjugate]] + z12*Im[z3*z4\[Conjugate]])/Im[z34*z12\[Conjugate]]]
incenter, circumcenter, inradius, ... .
For the Clifford circle theorems I needed second intersection: Given centers of circles though the origin z1, z2,
secondintersection[z1_, z2_] := (Conjugate[z1] z2 - Conjugate[z2] z1)/Conjugate[z1 - z2]
Is this obvious to anybody? I had to derive it with 8th grade analytic geometry. --rwg