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Discussion: Roundtable
Topic: "Graphing Calculator" Software


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Subject:   Parametric equation tools? Lissajous figures.
Author: Gene
Date: Oct 4 2003
I'm looking for a tool that allows you to specify x=f(t), y=g(t), the range of
t, and will not only graph (f(t),g(t)) but also show a little marker tracing out
the curve so you know where you are at time t (I guess you also need to be able
to vary the speed somehow).

The IES site has some things on parametric curves catalogued on Math Tools.
Their Parametric Equations is perhaps closest to what I want,
http://mathforum.org/mathtools/tool.html?co=c&tp=15.1.1&new_id=614/

For my class, however, I used Graphing Calculator, since my students have used
it and it is fairly flexible if a bit clunky on this topic. See the support
document "Learning Math" that comes with the program for more details, but here
are some things I showed.

First, choose "2-vector" from the Math menu, then set it equal to another
2-vector. In the second change x to sin nt and y to cos nt, so you have a
vertical version of [x,y] = [sin nt, cos nt]. This gives you a hunk of the graph
of a circle. If you click on the n at below the graph you get a dialog box that
gives you a chance to change the highest value of the slider variable n to 6.2
(2 pi) and the number of steps to 100. Then the graph will march around the unit
circle in 100 steps (slow enough to be seen) Note pause on slider bar and
ability to grab and move slider).

Students were interested when [sin nt, cos nt] was changed to [2sin nt, cos nt]
and amazed when it was changed to [sin 2nt, cos nt]. This does, in fact give you
the possibility of tracing Lissajous figures. Students appeared turned on and I
even got in a little about finding derivatives in this context.

This is a case where I used a wonderful general-purpose tool near the limit of
its capabilities. It would be nice to have a single-purpose tool focused on
this particular area.


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