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Enhanced Animations & Flipbooks
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Mathematica code as it appeared in Mathematica in Education,
Volume 2 Number 1, Fall 1992
;[s]
4:0,0;11,1;35,2;61,3;89,-1;
4:1,13,10,Times,2,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,13,10,Times,2,14,0,0,0;1,13,10,Times,0,14,0,0,0;
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Carl Swenson
Department of Mathematics
Seattle University
Seattle, WA 98122±4460
swenson@seattleu.edu
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(Mathematica version 2.1)
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*)
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Surface of Revolution animation code.
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First plot of 1 - x^2 in 3D
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(* First plot 1-x^2 function in 3D*)
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Table of plots
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(* ================= Table of plots ================== *)
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{t,0,.01+n*twoPi/11},
DisplayFunction->Identity,
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MathPictureEnd
:[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup; ]
The Unformatted text for this cell was not generated.
Use options in the Actions Preferences dialog box to
control when Unformatted text is generated.
;[o]
-Graphics-
:[font = section; inactive; Cclosed; preserveAspect; startGroup; ]
Surface of Revolution with Disks
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
First plot of 1 - x^2
:[font = input; initialization; preserveAspect; endGroup; ]
*)
(* First plot 1-x^2 function in 3D*)
f[x_]:=1-x^2
plot1=Show[
ParametricPlot3D[{t,0,f[t],Thickness[.01]},
{t,0,1},DisplayFunction->Identity],
Graphics3D[Line[{{0,0,1},{0,0,0}}]],
PlotRange->{{-1,1},{-1,1},{0,1}},
Axes->False
];
(*
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Function to create a disk of radius r
:[font = input; initialization; preserveAspect; endGroup; ]
*)
(* function to create a disk of radius r *)
twoPi=2Pi//N; (* speeds up calculations *)
onedisk[r_,top_,bottom_,dt_]:=
Graphics3D[
{SurfaceColor[GrayLevel[(r+0.5)/1.5],GrayLevel[.4],10],EdgeForm[],
Table[{
Polygon[{
{0,0,top},
{r Sin[t], r Cos[t],top},
{r Sin[t+dt],r Cos[t+dt],top}}],
Polygon[{
{r Sin[t], r Cos[t],bottom},
{r Sin[t+dt],r Cos[t+dt],bottom},
{r Sin[t+dt],r Cos[t+dt],top},
{r Sin[t], r Cos[t],top}
}]},
{t,dt,twoPi,dt}]
}
];
(*
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Create sound function
:[font = input; initialization; preserveAspect; endGroup; ]
*)
(* Create sound function *)
tone[m_]= (* well-tempered tuning, A with 3 overtones *)
Sin[twoPi*220*(2.^(m/12))*t]+
Sin[twoPi*220*(2.^(m/12))*2t]+
Sin[twoPi*220*(2.^(m/12))*4t]+
Sin[twoPi*220*(2.^(m/12))*8t];
(*
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Initial page setup
:[font = input; preserveAspect; endGroup; ]
(* =============== Initial page setup ================ *)
(* Set the page dimensions and partition *)
(* This is a 3x4 array in a 7.0x8.9 inch box *)
w=7.0;h=8.9;dw=w/3;dh=h/4;
(* Create the border and inlines *)
border={ AbsoluteThickness[1],
Line[{{0,0},{w,0},{w,h},{0,h},{0,0}}]};
inlines=Join[ {AbsoluteThickness[1]},
Map[Line,Table[{{0,j},{w,j}},{j,dh,h-dh,dh}]],
Map[Line,Table[{{i,0},{i,h}},{i,dw,w-dw,dw}]]
];
(* Create the coordinates for rectangles *)
coord1=Flatten[ Table[{i,j-dh},
{j,h,dh,-dh},{i,0,w-dw,dw}],1];
coord2=Flatten[ Table[{i+dw,j},
{j,h,dh,-dh},{i,0,w-dw,dw}],1];
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Table of plots
:[font = input; preserveAspect; endGroup; ]
(* ================= Table of plots ================== *)
disks={};dy=.09;
frames=Table[
AppendTo[disks,
onedisk[(1-dy*n)^.5,dy*n,dy*(n-1),twoPi/(25-n)]];
Show[plot1,disks,
PlotRange->{{-1,1},{-1,1},{0,1}},
DisplayFunction->Identity],
{n,1,11} ];
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Title/text frames created
:[font = input; preserveAspect; endGroup; ]
(* =========== Title/text frames created ============= *)
frame1=Show[
Graphics[{
Text[
FontForm["Solid of Revolution:",{"Times-Bold",18}],
Scaled[{.5,.9}]],
Text[ "f(x) = 1-x^2 on [0,1]",Scaled[{.5,.6}]],
Text[ "revolved about the y-axis.",Scaled[{.5,.4}]],
Text[ "- Approximated by disks -",Scaled[{.5,.10}]]
}],
DefaultFont->{"Times-Bold",14},
DisplayFunction->Identity ];
(* Use PrependTo[] to add frame(s) to front of list *)
(* Add Title frame or other special frames *)
PrependTo[frames,frame1];
(* Use AppendTo[] to add to the end of a frame list *)
(* To leave a frame blank use: AppendTo[frames,Graphics[]] *)
(* ============ Setup frames as Rectangles =========== *)
(* The list of frames must have 12 elements *)
(* The Rectangles are assigned array elements *)
frames=MapThread[Rectangle,{coord1,coord2,frames}];
:[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ]
Show the complete page
:[font = input; Cclosed; preserveAspect; startGroup; ]
(* ============= Show the complete page ============== *)
Show[
Graphics[border], (* sets page sizes *)
AspectRatio->h/w,
Epilog->Join[frames,inlines,border],
DisplayFunction->$DisplayFunction
];
(* Pull the graphic image to width 7.5 inches and print *)
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 505; pictureHeight = 642; endGroup; endGroup; endGroup; endGroup; ]
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