Poretsky's Law

Author

Eric W. Weisstein
July 10, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Logic/PoretskysLaw.nb.

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

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

Figure

xform[s_]:=(Circle[{xx_,yy_},rr_]:>s((x-xx)^2+(y-yy)^2-rr^2)<0)

Off[Intersection::"normal"];

Show[Graphics[With[{r=.6,R=1,n=2},
v=Table[Circle[r{Cos[#],Sin[#]}&[2Pi(i-1)/n],R],{i,n}];
{
Table[
InequalityPlot[{
v[[1]]/.xform[(-1)^(i+1)],
v[[2]]/.xform[(-1)^i]},
{x},{y},Axes->False,
Curves->None,
Fills->{Yellow,Green}[[i]],
DisplayFunction->Identity][[1]],{i,2}],
v,
Text[A⋂OverBar[B],{-.9,0},TextStyle->TraditionalForm],
Text[OverBar[A]⋂B,{.9,0},TextStyle->TraditionalForm]
}
],AspectRatio->Automatic]]