Trident of Descartes

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/TridentofDescartes.nb.

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Plot

ParametricPlot[{{t,(2+t)(2-t)(4-t)/(2t)},{-t,(2-t)(2+t)(4+t)/(-2t)}},{t,-6,-.1},Ticks->None,AspectRatio->Automatic,PlotRange->{{-5,5},{-5,5}},PlotStyle->Red]

Show[Function[a,ParametricPlot[{{t,(a+t)(a-t)(2a-t)/(a t)},{-t,(a-t)(a+t)(2a+t)/(-a t)}},{t,-6,-.1},Ticks->None,AspectRatio->Automatic,PlotRange->{{-5,5},{-5,5}},PlotStyle->Hue[a/3]]]/@Range[.5,3,.5]]