Epispiral Inverse Curve

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

InverseCurve[{Cos[t]a/Cos[n t],Sin[t]a/Cos[n t]},{0,0,k},t]//Simplify

Epispiral Inverse (@Center)

icurve[{x_,y_},{a_,b_},k_,sgn_]:=InverseCurvePlot[{sgn Cos[t]Sec[2 t],sgn Sin[t]Sec[2 t]},{x,y,k},{t,a,b}]

Show[Block[{$DisplayFunction=Identity},
{
icurve[{0,0},{-Pi/4+.01,Pi/4-.01},1,1],
icurve[{0,0},{-Pi/4+Pi/2+.01,Pi/4+Pi/2-.01},1,1],
icurve[{0,0},{-Pi/4+.01,Pi/4-.01},1,-1],icurve[{0,0},{-Pi/4+Pi/2+.01,Pi/4+Pi/2-.01},1,-1]
}],DisplayFunction->$DisplayFunction]