Spiric Section

Author

Eric W. Weisstein
December 9, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SolidGeometry/SpiricSection.nb.

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

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

Code

SpiricSection[a_,c_,r_]:=(r^2-a^2+c^2+x^2+y^2)^2==4c^2(x^2+r^2);

Show[GraphicsArray[{
{ImplicitPlot[SpiricSection[1,3,0],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,3,1.8],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,3,2],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,3,2.2],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-1.1,1.1}}]
},
{
ImplicitPlot[SpiricSection[1,1,0],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-2.1,2.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,1,.2],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-2.1,2.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,1,.4],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-2.1,2.1},{-1.1,1.1}}],ImplicitPlot[SpiricSection[1,1,1],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-2.1,2.1},{-1.1,1.1}}]
},
{
ImplicitPlot[SpiricSection[3,1,0],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-3.1,3.1}}],ImplicitPlot[SpiricSection[3,1,.4],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-3.1,3.1}}],ImplicitPlot[SpiricSection[3,1,1.2],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-3.1,3.1}}],ImplicitPlot[SpiricSection[3,1,2],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},DisplayFunction->Identity,PlotRange->{{-4.1,4.1},{-3.1,3.1}}]
}
}],DisplayFunction->$DisplayFunction]

Ring

Export["Phosphine:MathOztex:gifs:spiricr.gif",
Table[ImplicitPlot[SpiricSection[1,3,r],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},
PlotRange->{{-4.1,4.1},{-1.1,1.1}}
],{r,0,4,.2}],"GIF",ImageSize->400,AnimationDirection->ForwardBackward]

Horn

Export["Phosphine:MathOztex:gifs:spirich.gif",
Table[ImplicitPlot[SpiricSection[1,1,r],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},
PlotRange->{{-2.1,2.1},{-1.1,1.1}}
],{r,0,2,.1}],"GIF",ImageSize->400,AnimationDirection->ForwardBackward]

Spindle

Export["Phosphine:MathOztex:gifs:spirics.gif",
Table[ImplicitPlot[SpiricSection[3,1,r],{x,-5,5},
Ticks->None,AspectRatio->Automatic,AxesOrigin->{0,0},
PlotRange->{{-4.1,4.1},{-3.1,3.1}}
],{r,0,4,.2}],"GIF",ImageSize->400,AnimationDirection->ForwardBackward]