(*^ ::[paletteColors = 128; automaticGrouping; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L1, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; ; fontset = message, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = print, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = info, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 12, "Courier"; ; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 10, "Times"; ; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = Left Header, nohscroll, cellOutline, 12; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, L1, 12; fontset = Left Footer, cellOutline, blackBox, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12;] :[font = title; inactive; preserveAspect; startGroup; ] Plotting in Polar Coordinates :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] PolarAnimation Module :[font = input; preserveAspect; ] Clear[PolarAnimation] PolarAnimation[r_, {T1_, T2_, dT_}, opts___Rule] := Module[ {q, T}, Do[ string = StringForm["`1` Pi", N[T/Pi]]; label = FontForm[string, {"Times-Bold", 16}]; q = {Cos[T], Sin[T]}; ParametricPlot[ {r[t] Cos[t], r[t] Sin[t]}, {t, 0, T}, opts, PlotLabel -> label, AspectRatio -> Automatic, Axes -> Automatic, Epilog -> Show[Graphics[{PointSize[0.03], Point@q}], DisplayFunction -> Identity ] [[1]] ], {T, T1, T2, dT}] ] :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] Example :[font = input; preserveAspect; endGroup; endGroup; ] k = 2; r[t_] := Sin[k t] PolarAnimation[r, {Pi/4, 2Pi, Pi/4}, PlotRange -> {{-1.1, 1.1}, {-1.1, 1.1}} ] :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Introductory Example :[font = input; preserveAspect; ] < 75 ] :[font = input; preserveAspect; ] PolarPlot[Sin[Sqrt[2]t], {t, 0, 24Pi}, PlotPoints -> 75 ] :[font = input; preserveAspect; endGroup; ] PolarPlot[Sin[Sqrt[2]t], {t, 0, 48Pi}, PlotPoints -> 75 ] :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] 1 + p Sin(theta) :[font = input; preserveAspect; ] p = 3/4; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 1; PolarPlot[1 +p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 4/3; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 1/2; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 1/4; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 0; PolarPlot[1 +p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] p = 4; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = input; preserveAspect; endGroup; ] p = 16; PolarPlot[1 + p Sin[t], {t, 0, 2Pi}] :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] Creative Plots :[font = input; preserveAspect; ] niceplot[t_] := 3 Cos[t]^2 - 1 PolarPlot[niceplot[t], {t, 0, 2Pi}] :[font = input; preserveAspect; ] niceplot[t_] := 3 Cos[t]^3 - 1 PolarPlot[niceplot[t], {t, 0, 2Pi}] :[font = input; preserveAspect; endGroup; endGroup; ] niceplot[t_] := 3 Cos[3t/4]^3 - 1 PolarPlot[niceplot[t], {t, 0, 8Pi}, PlotPoints -> 75 ] ^*)