Plane Division by Ellipses

Author

Eric W. Weisstein
December 10, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComputationalGeometry/PlaneDivisionbyEllipses.nb.

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

©2010 Wolfram Research, Inc. except for portions noted otherwise

Counts

Table[2n^2-2n+2,{n,10}]

Figure

ellipse=Circle[{0,0},{1,.5}];

c={2,6,14,26};

Row[Table[Column[{c[[k]],Graphics[Table[Rotate[ellipse,n π/k],{n,0,k-1}]],Row[{Style["n",Italic]," == ",ToString[k]}]},Alignment->Center],{k,4}]]//TraditionalForm

GraphicsGrid[{c,
Table[Graphics[Table[Rotate[ellipse,n π/k],{n,0,k-1}]],{k,4}],
Table[Row[{Style["n",Italic]," == ",ToString[k]}],{k,4}]
},Spacings->{Automatic,-100}]