(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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cylindrical coordinates. This will be useful when we want to \ plot a surface that has radial symmetry about an axis. Cylindrical \ coordinates are related to Cartesian coordinates by the following \ equations.\ \>", "Text"], Cell[TextData[{ StyleBox["x", FontSlant->"Italic"], " = ", StyleBox["r", FontSlant->"Italic"], " cos(\[Theta])\n", StyleBox["y", FontSlant->"Italic"], " = ", StyleBox["r", FontSlant->"Italic"], " sin(\[Theta])\n", StyleBox["z", FontSlant->"Italic"], " = ", StyleBox["z", FontSlant->"Italic"] }], "Text"], Cell["as show in the following illustration.", "Text"], Cell[BoxData[ \(drawCylindrical[]\)], "Input"], Cell[TextData[{ "For a start, we ought to be able to draw a cylinder using cylindrical \ coordinates, or else cylindrical coordinates don't deserve their name. ", "Replace the asterisks below with the correct formulas to generate a ", " cylinder of radius 3 with its axis along the ", StyleBox["z", FontSlant->"Italic"], " axis." }], "Text"], Cell[BoxData[{ \(Clear[x, y, z, u, v]\), "\[IndentingNewLine]", \(\(x[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(y[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(z[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 0, 2 \[Pi]}, {v, 0, 10}, ViewPoint \[Rule] {3, 2, 2}, AxesLabel \[Rule] {"\", "\", "\"}, PlotPoints \[Rule] {60, 30}];\)\)}], "Input"], Cell[TextData[{ "Now, try to create a cylinder of radius 3 with its axis along the ", StyleBox["y", FontSlant->"Italic"], " axis." }], "Text"], Cell[BoxData[{ \(Clear[x, y, z, u, v]\), "\[IndentingNewLine]", \(\(x[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(y[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(z[u_, v_] := ** ;\)\), "\[IndentingNewLine]", \(\(ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 0, 2 \[Pi]}, {v, 0, 4}, ViewPoint \[Rule] {3, 2, 2}, AxesLabel \[Rule] {"\", "\", "\"}, PlotPoints \[Rule] {60, 30}];\)\)}], "Input"], Cell["\<\ Try to predict what the following graph will look like, before you \ evaluate the cell.\ \>", "Text"], Cell[BoxData[{ \(Clear[r, x, y, z, u, v]\), "\[IndentingNewLine]", \(r[u_, v_] := 2 + Sin[6 v]\), "\[IndentingNewLine]", \(x[u_, v_] := r[u, v]\ Cos[u]\), "\[IndentingNewLine]", \(y[u_, v_] := r[u, v]\ Sin[u]\ \), "\[IndentingNewLine]", \(z[u_, v_] := v\), "\[IndentingNewLine]", \(\(ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 0, 2 \[Pi]}, {v, 0, 8}, ViewPoint -> {7, \ \(-5\), \ 4}, AxesLabel \[Rule] {"\", "\", "\"}, PlotPoints \[Rule] {20, 120}];\)\)}], "Input"], Cell[TextData[{ StyleBox["Exercise 6.3:", FontWeight->"Bold", FontColor->RGBColor[0, 0.500008, 0.250004]], " Create a graph that looks like a string of 12 pearls. Each pearl should \ have a length of 0.05 and a diameter of 0.05. The pearls do not have to be \ perfect spheres." }], "Text", Background->GrayLevel[0.750011]] }, Closed]] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1920}, {0, 1127}}, AutoGeneratedPackage->None, WindowSize->{904, 640}, WindowMargins->{{0, Automatic}, {Automatic, 3}}, StyleDefinitions -> "PastelColor.nb" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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