Arachnida

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Additional Authors

Original version by Margherita Barile
June 18, 2002

Plot

Arachnia1[a_,n_][θ_]:=a ((Sin[n θ])/(Sin[(n-1)θ])){Cos[θ],Sin[θ]}

Arachnia2[a_,n_][θ_]:=a ((Sin[n θ])/(Sin[(n+1)θ])){Cos[θ],Sin[θ]}

V5

<<Graphics`Graphics`

Show[GraphicsArray[PolarPlot[#,{t,0,Pi},
PlotStyle->Red,
PlotRange->{{-1,2},{-2,2}},
Ticks->False,
PlotLabel->TraditionalForm[#/.Csc[x_]:>1/sin[x]],
DisplayFunction->Identity]&/@
{Sin[2t]/Sin[3t],Sin[3t]/Sin[2t]}
]
]

V6

With[{n=3},PolarPlot[((Sin[n θ])/(Sin[(n-1)θ])),{θ,-π/2,π/2},ImageSize->{Automatic,200}]]

ParametricPlot[Arachnia1[1,#][t],{t,0,10π}]&/@{.3,.5,2,2.5,3}

ParametricPlot[Arachnia1[1,#][t],{t,0,10π},Exclusions->Range[-10,10]Pi]&/@{.3,.5,2,2.5,3}

ParametricPlot[Arachnia2[1,#][t],{t,0,10π}]&/@{.3,.5,2,2.5,3}