Dissection Fallacy

Author

Eric W. Weisstein
March 26, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/DissectionFallacy.nb.

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

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

Graphics

<<Graphics`Colors`;

FilledPolygon[l_List,gr_:GrayLevel[.5]]:={{gr,Polygon[l]},Line[Append[l,First[l]]]}

Grid[x_,y_]:={Table[Line[{{-1,n},{x,n}}],{n,0,y}],
Table[Line[{{n,-1},{n,y}}],{n,0,x}]}

Show[GraphicsArray[Graphics[#,AspectRatio->Automatic]&/@{{
FilledPolygon[{{0,0},{8,0},{8,3}},Red],
FilledPolygon[{{0,0},{0,3},{8,3}},Yellow],
FilledPolygon[{{0,3},{0,8},{3,8},{5,3}},Green],
FilledPolygon[{{3,8},{8,8},{8,3},{5,3}},Blue],
Grid[9,9]
},
{
FilledPolygon[{{0,0},{5,0},{3,5},{0,5}},Green],
FilledPolygon[{{3,5},{0,5},{0,13}},Yellow],
FilledPolygon[{{0,13},{5,13},{5,8},{2,8}},Blue],
FilledPolygon[{{5,8},{2,8},{5,0}},Red],
Grid[6,14]
},
{
FilledPolygon[{{0,8},{5,8},{3,13},{0,13}},Green],
FilledPolygon[{{3,13},{6,13},{6,5}},Red],
FilledPolygon[{{6,5},{11,5},{11,0},{8,0}},Blue],
FilledPolygon[{{5,8},{8,0},{5,0}},Yellow],
Grid[12,14]
}
}]]

Lengths

Show[Graphics[{
FilledPolygon[{{0,0},{5,0},{3,5},{0,5}},Green],
FilledPolygon[{3.8,0}+#&/@{{0,5},{5,5},{5,0},{2,0},{2,0},{0,5}},Blue],
FilledPolygon[{0,-.7}+#&/@{{0,0},{8,0},{0,-3},{0,0}},Yellow],
{Dashing[{.02}],
Line[{{3,0},{3,5}}],Line[{{5.8,0},{5.8,5}}]
}
}],AspectRatio->Automatic]