Spiral

Author

Eric W. Weisstein
June 9, 2024

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

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

©2024 Wolfram Research, Inc. except for portions noted otherwise

Figure

spirals={
{"Archimedean spiral",(θ^(3/2)),0,4π,Automatic},
{"Archimedes' spiral",θ,0,4π,Automatic},
{"atom\[Hyphen]spiral",(θ/(θ-4)),4,6π,Automatic},
{"epispiral",Sec[2θ],.1,2π,π/4Range[8]},
{"Fermat's spiral",(θ^(1/2)),0,4π,Automatic},
{"Galilean spiral",-θ^2-1,0,4π,Automatic},
{"hyperbolic spiral",1/θ,0,4π,Automatic},
{"lituus",(θ^(-1/2)),0,4π,Automatic},
{"logarithmic spiral",Exp[.2θ],0,6π,Automatic}
};
GraphicsGrid[Partition[PolarPlot[#2,{θ,#3,#4},PlotLabel->#1,Ticks->None,Exclusions->#5,PlotStyle->Red,LabelStyle->Directive[14,Black,Italic,FontFamily->"Times"]]&@@@spirals,UpTo[4]],Alignment->Top,ImageSize->700,Dividers->All]