Square Quadrants

Author

Eric W. Weisstein
July 16, 2002

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

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

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

Initialization

<<Calculus`Integration`;
<<Graphics`InequalityGraphics`;

Geometric

ExpandAll[Solve[{{1,4,4},{1,3,2},{1,2,1}}.{a,b,c}=={1,π/4,π/3-Sqrt[3]/4},{a,b,c}]][[1]]//ColumnForm

Algebraic

InequalityPlot[And@@((x-#1)^2+(y-#2)^2<1&@@@Flatten[Outer[List,{0,1},{0,1}],1]),{x},{y},Axes->False]

ExpandAll[Integrate[Boole[And@@((x-#1)^2+(y-#2)^2<1&@@@Flatten[Outer[List,{0,1},{0,1}],1])],{x},{y}]]

InequalityPlot[(x-1)^2+y^2<1&&x^2+(y-1)^2<1&&(x-1)^2+(y-1)^2>1,{x},{y},Axes->False]

ExpandAll[Integrate[Boole[(x-1)^2+y^2<1&&x^2+(y-1)^2<1&&(x-1)^2+(y-1)^2>1],{x},{y}]]

InequalityPlot[(x-1)^2+y^2>1&&(x-1)^2+(y-1)^2>1&&x>0&&y>0,{x},{y}]

ExpandAll[Integrate[Boole[(x-1)^2+y^2>1&&(x-1)^2+(y-1)^2>1&&x>0],{x},{y}]]

InequalityPlot[(x-1)^2+y^2>1&&(x-1)^2+(y-1)^2>1&&0<x<1&&0<y<1,{x},{y}]

ExpandAll[Integrate[Boole[(x-1)^2+y^2>1&&(x-1)^2+(y-1)^2>1&&0<x<1&&0<y<1],{x},{y}]]