Polar Triangle

Author

Eric W. Weisstein
January 30, 2005

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

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

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

Definition

Factor[4#]&/@PolarTriangle[(a11 α^2+a22 β^2+a33 γ^2+a12 α β+a23 β γ+a31 α γ)]

Table

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

l=Function[tri,Print[l0={tri,TimeConstrained[Select[Triangles,Cartesian[PolarTriangle[tri][t]]==#[t]&],60]//Timing}];l0]/@Sort[Join[CentralCircles,Conics]];

DisplayForm[Grid[Sort[{Name[#[[1]]],
If[#[[-1,-1]]==={}||#[[-1,-1]]===$Aborted,"*",Name[#[[-1,-1,1]]]]}&/@l],RowLines->True,ColumnAlignments->Left]]