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Mathematica Animations by High School Students

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  • Subject: [mg101996] Mathematica Animations by High School Students
  • From: Helen Read <hpr at>
  • Date: Sun, 26 Jul 2009 03:53:45 -0400 (EDT)
  • Reply-to: HPR <read at>

You might enjoy looking at some Mathematica animations created by a 
group of 30 very bright high school students at the Vermont Governor's 
Institute in Mathematical Sciences about a month ago. (I meant to post 
the link here sooner, but am just now getting around to it.)

The students had no previous exposure to Mathematica, and I had them for 
only a single 75-minute session. We made liberal use of the Classroom 
Assistant palette so that I didn't have to teach them much syntax. I 
began by showing them how to use ContourPlot to make a static plot of 
familiar equations (lines, circles, parabolas, etc.). Then we discussed 
the idea of introducing a parameter into an equation so that we could 
animate it in some way (e.g., change the slope of a line or move it up 
and down, that sort of thing). Then we took a ContourPlot of two lines, 
one horizontal and one vertical, threw in a parameter and wrapped 
Animate around the whole thing, to make the vertical line move from left 
to right. I then told them to see if they could get the horizontal line 
to move from top to bottom at the same time the vertical was moving left 
to right. I gave them a few suggestions of other things to try, and they 
took it from there. A few helpers and I walked around the room helping 
out and answering questions.

I have taught week long Mathematica course at the Math Institute in past 
years, but this was the first time that I did it only a single session. 
The Classroom Assistant palette was a big help in that regard. Also, 
using ContourPlot (which might seem an odd choice) worked very well. I 
wanted them to be able to plot circles, ellipses, vertical lines, etc., 
and didn't have time to teach them about parametric equations the way I 
would have if we had all week. With ContourPlot they could put in 
familiar Cartesian equations, and all of them came up with at least one 
neat animation within the time that we had. Some of the older kids with 
a bit more math behind them asked if it's possible to plot polar curves 
("Yes! Here, let me show you where to find PolarPlot on the palette"), 
and a few of them made some 3D animations.

Here are some of the students' animations. Enjoy.

One minor aggravation in all this: I find it baffling that exporting an 
animation from Animate or Manipulate from Mathematica into any video 
format results in the animation running forward and then backward. I 
have not found any way to get it to export so that it runs once in the 
forward direction only. The kids' animations look OK going forward and 
back, but there some things we would really like to run in one direction 
only. AnimationDirection->Forward doesn't do anything when you export, 
as far as I can tell.

Helen Read
University of Vermont

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