(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[      4073,        124]
NotebookOptionsPosition[      3598,        104]
NotebookOutlinePosition[      4056,        122]
CellTagsIndexPosition[      4013,        119]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["PolarPath", "Title",
 CellChangeTimes->{{3.389027944836617*^9, 3.38902794627962*^9}},
 TextAlignment->Center],

Cell[TextData[{
 "For this animation, you are welcome to change the function ",
 StyleBox["r",
  FontSlant->"Italic"],
 " as well as the values of ",
 StyleBox["thetamin",
  FontSlant->"Italic"],
 " and ",
 StyleBox["thetamax",
  FontSlant->"Italic"],
 " (shown in magenta below), the starting and stopping values for \[Theta]. "
}], "Text",
 CellChangeTimes->{{3.3890279570088053`*^9, 3.389028032888001*^9}, {
  3.692575864083555*^9, 3.6925758734542*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"r", "[", "\[Theta]_", "]"}], ":=", 
   RowBox[{"Cos", "[", 
    RowBox[{"4", "\[Theta]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"thetamin", " ", "=", " ", 
   StyleBox["0",
    FontColor->RGBColor[1, 0, 1]]}], ";", " ", 
  RowBox[{"thetamax", " ", "=", " ", 
   StyleBox[
    RowBox[{"2", "\[Pi]"}],
    FontColor->RGBColor[1, 0, 1]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"polargr", "=", 
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"PolarPlot", "[", 
      RowBox[{
       RowBox[{"r", "[", "\[Theta]", "]"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"\[Theta]", ",", " ", "thetamin", ",", " ", "thetamax"}], 
        "}"}]}], "]"}], ",", " ", 
     RowBox[{"PlotRange", "\[Rule]", "Automatic"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Manipulate", "[", 
   RowBox[{
    RowBox[{"PolarPlot", "[", 
     RowBox[{
      RowBox[{"r", "[", "\[Theta]", "]"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"\[Theta]", ",", " ", "thmin", ",", " ", "k"}], "}"}], ",", 
      " ", 
      RowBox[{"Evaluate", "@", 
       RowBox[{"AbsoluteOptions", "[", 
        RowBox[{"polargr", ",", "PlotRange"}], "]"}]}], ",", " ", 
      RowBox[{"PlotStyle", "\[Rule]", "Thick"}], ",", " ", 
      RowBox[{"ColorFunction", "\[Rule]", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"Hue", "[", "#3", "]"}], "&"}], ")"}]}], ",", " ", 
      RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}], ",", " ", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"k", ",", 
        RowBox[{"thetamin", "+", ".01"}], ",", " ", "\"\<theta\>\""}], "}"}], 
      ",", " ", 
      RowBox[{"thetamin", "+", ".01"}], ",", " ", "thetamax"}], "}"}]}], 
   "]"}], " "}]}], "Input",
 CellChangeTimes->{{3.3889364613810463`*^9, 3.388936579939974*^9}, {
   3.3889366577298183`*^9, 3.388936774674656*^9}, {3.3889368056194277`*^9, 
   3.3889368456096363`*^9}, 3.388936886277131*^9, {3.388936926668614*^9, 
   3.388936957473858*^9}, {3.3889370497595387`*^9, 3.388937071260337*^9}, {
   3.394921806063964*^9, 3.394921854539607*^9}, {3.394922066805509*^9, 
   3.394922111547195*^9}, {3.3949221901412354`*^9, 3.394922228048799*^9}, {
   3.394922305395471*^9, 3.394922311189127*^9}, {3.4431853874233923`*^9, 
   3.4431854088278303`*^9}, {3.443185752266737*^9, 3.4431857854310493`*^9}, {
   3.692575896777516*^9, 3.692575926646224*^9}}]
}, Open  ]]
},
WindowSize->{813, 806},
WindowMargins->{{631, Automatic}, {Automatic, 219}},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
Magnification->1.,
FrontEndVersion->"11.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \
21, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 115, 2, 92, "Title"],
Cell[685, 26, 456, 13, 49, "Text"],
Cell[1144, 41, 2438, 60, 138, "Input"]
}, Open  ]]
}
]
*)