Epispiral

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Plot

<<Graphics`Graphics`

EpispiralRanges[n_?EvenQ]:=Join[{0},Range[1,4n-1,2],{4n}]
EpispiralRanges[n_?OddQ]:=Range[1,4n-1,2]

EpispiralPlot[n_,opts___]:=Show[
Block[{$DisplayFunction=Identity},
PolarPlot[Sec[n t],Evaluate[{t,Sequence@@#}],PlotStyle->Red]&/@(Partition[EpispiralRanges[n],2,1]Pi/(2n))],
opts,Ticks->None
]

MakeBoxes[label[n_],TraditionalForm]:=RowBox[{"n","==",MakeBoxes[n,TraditionalForm]}]

Show[GraphicsArray[
Block[{$DisplayFunction=Identity},
Partition[Table[
EpispiralPlot[n,PlotLabel->TraditionalForm[label[n]],PlotRange->{{-1,1},{-1,1}}5],{n,2,9}],4]]]
]

AbsEpispiralPlot[n_,opts___]:=Show[
Block[{$DisplayFunction=Identity},
PolarPlot[Abs[Sec[n t]],Evaluate[{t,Sequence@@#}],PlotStyle->Red]&/@(Partition[Join[{0},Range[1,4n-1,2],{4n}],2,1]Pi/(2n))],
opts,Ticks->None
]

Show[GraphicsArray[
Block[{$DisplayFunction=Identity},
Partition[Table[
AbsEpispiralPlot[n,PlotLabel->TraditionalForm[label[n]],PlotRange->{{-1,1},{-1,1}}5],{n,2,9}],4]]]
]