Re: Archimedes' Spiral
- To: mathgroup at smc.vnet.net
- Subject: [mg85636] Re: Archimedes' Spiral
- From: "David Park" <djmpark at comcast.net>
- Date: Sat, 16 Feb 2008 03:32:05 -0500 (EST)
- References: <fp3uad$9gf$1@smc.vnet.net>
Lea,
We can obtain the parametrization for Archimedes spiral from Alfred Gray's
excellent book 'Modern Differential Geometry of Curves and Surfaces with
Mathematica: Second Edition'.
archimedesspiral[n_, a_][t_] := a t^(1/n) {Cos[t], Sin[t]}
With[{n = 1, a = 1},
ParametricPlot[archimedesspiral[n, a][t], {t, 0, 6 \[Pi]},
Frame -> True,
Axes -> False,
PlotLabel -> "Archimedes Spiral",
Epilog -> {Text[HoldForm["a" == a], Scaled[{.80, .95}], {-1, 0}],
Text[HoldForm["n" == n], Scaled[{.80, .9}], {-1, 0}]},
BaseStyle -> {FontSize -> 12}]
]
For those who have the Presentations package we can also draw the curve as a
complex expression in the complex plane and dispense with Epilog.
Needs["Presentations`Master`"]
With[{n = 1, a = 1},
Draw2D[
{ComplexCurve[a t^(1/n) \[ExponentialE]^(\[ImaginaryI] t), {t, 0, 6
\[Pi]}],
Text[HoldForm["a" == a], Scaled[{.80, .95}], {-1, 0}],
Text[HoldForm["n" == n], Scaled[{.80, .9}], {-1, 0}]},
Frame -> True,
PlotLabel -> "Archimedes Spiral",
BaseStyle -> {FontSize -> 12}]
]
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"Lea Rebanks" <lrebanks at netvigator.com> wrote in message
news:fp3uad$9gf$1 at smc.vnet.net...
> Hi All,
>
> I am trying to plot the Archimedes' Spiral.
>
> I copied this code from a web site. But it didn't work. Any ideas.
>
> ParaPlot[ArchimedeanSpiral[1][t],
> {t, 0, 10*2*Pi}, PlotDot ->
> False, AspectRatio -> Automatic,
> PlotLabel ->
> "Archimedes' spiral, r == theta"\
> , Ticks -> {Range[0, 60, 20],
> Range[0, 60, 20]},
> Background -> GrayLevel[0]];
> Do[ParaPlot[Evaluate[
> ArchimedeanSpiral[i][t]],
> {t, 0.0001, 5*2*Pi},
> PlotDot -> False, PlotPoints ->
> 30, AspectRatio -> Automatic,
> PlotRange -> {{-1, 1}, {-1, 1}}*
> (5*2*Pi)^i*1.1, PlotLabel ->
> StringForm["r == theta^``",
> PaddedForm[N[i], {4, 2}]],
> Ticks -> {{N[Floor[(4*2*Pi)^i]]},
> {N[Floor[(4*2*Pi)^i]]}},
> Background -> GrayLevel[0]],
> {i, 0, 2, 2/20}]
>
>
>
>
> Many thanks for your help & attention.
> Best Regards - Lea Rebanks...
>
>