Square Illusions

Author

Eric W. Weisstein
August 30, 2007

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

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Lines Illusion

RectangleBorder[{x1_,y1_},{x2_,y2_}]:=Line[{{x1,y1},{x2,y1},{x2,y2},{x1,y2},{x1,y1}}]

Show[GraphicsArray[Graphics[#2,
PlotLabel->TraditionalForm[#1],
AspectRatio->Automatic,PlotRange->All]&@@@{
{A,RectangleBorder[{0,0},{1,1}]},
{B,Line/@Table[{{x,0},{x,1}},{x,0,1,.05}]},
{C,Line/@Table[{{0,y},{1,y}},{y,0,1,.05}]}
}
]]

Orientation Illusion

Show[GraphicsArray[Graphics[#2,
PlotLabel->TraditionalForm[#1],
AspectRatio->Automatic,
PlotRange->{{-1,1},{-1,1}}]&@@@{
{A,Line@Table[{Cos[#],Sin[#]}&[2Pi i/4],{i,0,4}]},
{B,Line@Table[{Cos[#],Sin[#]}&[2Pi(i+1/2)/4],{i,0,4}]}
}]]

Horizontal-Vertical illusion

Show[GraphicsArray[Graphics[#2,
PlotLabel->TraditionalForm[#1],
AspectRatio->Automatic,
PlotRange->{{0,1},{0,1}}1.1]&@@@{
{A,RectangleBorder[{0,0},{1,.95}]},
{B,RectangleBorder[{0,0},{1.02,1.02}]}
},
GraphicsSpacing->-.1]]