Cyclocevian Triangle

Author

Eric W. Weisstein
January 21, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/CyclocevianTriangle.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CyclocevianTriangle.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Trilinear Vertex Matrix

CyclocevianTriangle[{α,β,γ}]

Derivation

Simplify[CevianTriangle[CyclocevianConjugate[{α,β,γ}]]]

Table

t=Triangle[Table[Random[Real,{0,1},50],{3},{2}]];
kc=KimberlingCenters;

Length[k=Vertices[Cartesian[CyclocevianTriangle[#][t]]]&/@kc]//Timing

l={};
Do[
Print[l0={
i,
p=Triangles[[i]],
tri=Vertices[p[t]];
kc[[Flatten[Position[k,_?(#==tri&)]]]]//Timing
}];
AppendTo[l,l0],
{i,Length[Triangles]}
]

Nicely Formatted

DisplayForm[Grid[{#[[-1,-1,1]],CenterName[#[[-1,-1,1]]],TriangleName[#[[2]]]}&/@Sort[Select[l,#[[-1,-1]]=!={}&],#1[[-1,-1,1,1]]<#2[[-1,-1,1,1]]&],
RowLines->True,ColumnAlignments->Left
]
]