Maltitude

Author

Eric W. Weisstein
April 20, 2004

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

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

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

Code

General

q=Quadrilateral[{{-0.1,0},{0,2},{-1.5,0.8},{-1,0}}];

Show[Graphics[{
q,
{Red,Maltitudes[q],
PerpSquare[#,.05,3]&/@Transpose[{Sides[q],Maltitudes[q]}]
},
{Blue,EqualSideTicksAboutMidpoints[q,.02,.02]},
PointLabels[Join[
Transpose[{VertexPoints[q],{"A","B","C","D"}}],
Append[#,Red]&/@Transpose[{EndPoint/@Maltitudes[q],{"(Subscript[M, CD])","(Subscript[M, DA])","(Subscript[M, AB])","(Subscript[M, BC])"}}],
{{Centroid[q],"G"}}
],PointSize[.03]]
}],AspectRatio->Automatic]

Cyclic

q=CyclicQuadrilateral[{.1,1.2,2.7,5.2}];

Show[Graphics[{
q,
{Blue,Circle[{0,0},1]},
{Red,Maltitudes[q],
PerpSquare[#,.05,3]&/@Transpose[{Sides[q],Maltitudes[q]}]
},
{Purple,Thickness[.01],Line[{{0,0},Coordinates[Anticenter[q]]}]},
PointLabels[Join[
Transpose[{VertexPoints[q],{"A","B","C","D"}}],
Append[#,Red]&/@Transpose[{EndPoint/@Maltitudes[q],{"(Subscript[M, CD])","(Subscript[M, DA])","(Subscript[M, AB])","(Subscript[M, BC])"}}],
{{Point[{0,0}],"O",Blue},{Centroid[q],"G"},{Anticenter[q],"T",Purple}}
],PointSize[.03]]
}],AspectRatio->Automatic]

Distance@@@({Centroid[q],#}&/@{Point[{0,0}],Anticenter[q]})