I have posted on abstractmath.org a CDF file of families of functions whose parameters you can control interactively. It is fascinating to play with them and see phenomena you (or at least I) did not anticipate.  Some of them have questions of the sorts you might ask students to discuss or work out.  Working out explanations for many of the phenomena demand some algebra skills, and sometimes more than that.

The Mathematica command that sets up one of the families looks like this:

Manipulate[
Plot[{Sin[a x], a Cos[a x]}, {x, -2 Pi, 2 Pi},
PlotRange -> {{-4, 4}, {-4, 4}}, PlotStyle -> {Blue, Red},
AspectRatio -> 1], {{a, 1}, -4, 4, Appearance -> “Labeled”}]

It would be straightforward to make a command something like

PlotFamily[functionlist, domain, plotrange]

with various options for colors, aspect ratio and so on that would do these graphs.  But I found it much to easy to simply cut and paste and put in the new inputs and parameters as needed.

This sort of Mathematica programming is not hard if you have an example to copy, but you do need to get over the initial hump of learning the basic syntax.   I know of no other language where it would be as easy as the example above to produce an interactive plot of a family of functions.

But many people simply hate to learn a new language.  If this sort of interactive example turns out to be worthwhile, someone could design an interface that would allow you to fill in the blanks and have the command constructed for you.  (I could say the same about some of other cdf files I have posted on this blog recently.) But that someone won’t be me.  I have too much fun coming up with new ideas for math  exposition to have to spend time working out all the details.  And all my little experiments are available to use under the Creative Commons License.

I would appreciate comments and suggestions.

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