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Cell["\<\
Mathematica has a large number of built-in graphics programs for plotting and \
exploring mathematics graphically and for plotting and visualizing data.  \
Graphs and plots are effective ways of conveying complex information.  It is \
important to learn how to create and manipulate plots and graphics.  \
Mathematica is very rich in its graphical functions\[LongDash]we will explore \
just a small subset of all its capabilities.  We can get an idea of how many \
plotting routines are available by using a wildcard:\
\>", "Text",
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Cell["\<\
While Mathematica has a large number of plotting routines, no one program \
does everything we need.  It can be useful to export numbers and graphics \
from Mathematica and operate on them individually or with other specialized \
programs.  The number of different creative graphical solutions available \
grows geometrically with the number of different graphical tools that are \
mastered.
Here, we will just produce a number of examples of plots and graphics... \
\>", "Text",
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Cell["\<\
Controlling Precision and Size: The Mesh
(And an example of Interactive Control over Plot Appearance--Manipulate)\
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Let's create a function that returns a list {x(t), y(t)} as a function of its \
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Cell["\<\
We can use Manipulate to view how the plot changes with the parameter n, and \
also change the last point drawn to see how the curve gets traced out.\
\>", "Text",
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{$CellContext`t, 0, $CellContext`lastp$$}, PlotStyle -> Thick, PlotPoints -> 
        6 $CellContext`ncirc$$, Axes -> False], 
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      "DefaultOptions" :> {}],
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Cell["\<\
To demonstrate Parametrtic plot of a region, let's create a function that \
returns a list {x(r,t), y(r,t)} as a function of its arguments r and t. We \
add a parameter n to make things interesting to look at...\
\>", "Text",
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Cell[BoxData[
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   RowBox[{"r_", ",", " ", "t_", ",", " ", "n_"}], "]"}], " ", ":=", "  ", 
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   RowBox[{
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     RowBox[{"r", " ", 
      RowBox[{"Cos", "[", 
       RowBox[{"n", " ", "t"}], " ", "]"}]}], " ", "+", " ", 
     RowBox[{"Cos", "[", "t", "]"}]}], ",", " ", 
    RowBox[{
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      RowBox[{"Sin", "[", 
       RowBox[{"n", " ", "t"}], "]"}]}], " ", "+", " ", 
     RowBox[{"Sin", "[", "t", "]"}]}]}], "}"}]}]], "Input",
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Cell["\<\
If we fix r, this is a one dimensional curve as above.\
\>", "Text",
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Cell[CellGroupData[{

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    RowBox[{"t", ",", 
     RowBox[{"-", "Pi"}], ",", " ", "Pi"}], "}"}], ",", 
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Cell["\<\
Now we let both r and t vary. Some regions in the disk r \[Element] \
(0.25,0.75) don't get covered, and others get covered one or more times.\
\>", "Text",
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