Discussion:  Roundtable 
Topic:  Your Favorite Tools 
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Subject:  RE: Favorite Tools 
Author:  Alan Cooper 
Date:  Aug 6 2004 
MathTools site itself, but I do have some to suggest.
My alltime favourite is still one of the ies group's java applets
"demonstrating" a proof of Pythagoras' Theorem. I put "demonstrating" in quotes
because the applet just gives the users the necessary tools to discover a proof
rather than actually telling them what to do. I think it's brilliant!
(see http://www.ies.co.jp/math/java/geo/pitha1/pitha1.html )
The same exploratory approach is taken in their proofs of the law of cosines and
of the trig sum rules and I also like their combined definitions and graphs of
the trig functions. They did each separately, but then following a suggestion of
Don Cohen they also did one applet showing all at once.
(for all of these see http://www.ies.co.jp/math/java/trig/ )
The construction of a graph by matching the ordinate with a correspondingly
coloured line segment also occurs in number three on my list  which comes from
the same source as well. It's their "surfer dude" demonstration of the graph of
the derivative. This one only does it for one function, but I think it has
enough features to make the ideas clear.
(see http://www.ies.co.jp/math/java/calc/doukan/doukan.html )
I could probably complete my full list without leaving the ies site, but perhaps
that really wouldn't be fair to the rest of the world.
Another one I like is the areasofar antiderivative applet at the
University of Vienna which works with a graph "drawn" by the user. Controlling
the shape is not quite as easy as one might like, but making it possible at all
is quite an achievement, and demonstrating the concept independently of formulas
is something I like to see.
(see http://www.univie.ac.at/future.media/moe/galerie/int/int.html #intuitiv
)
The university of Syracuse Physics Dep't has a very nice demo of the cross
product.
(see http://www.phy.syr.edu/courses/javasuite/crosspro.html )
Another version at MIT by Dan Kleitman (which is in the catalog, but I think
with the wrong url) has less attractive graphics but gives more options and
shows the determinant and coordinates. I'd call this a tie.(see
http://wwwmath.mit.edu/18.013A/HTML/tools/tools11.html )
My favourite implicit grapher is the one by Dana Gourley (see
http://www.geocities.com/CapeCanaveral/Runway/2360/ )
It produces great detail quite quickly and has a nice "colour dimension" option
for a third variable.
And I suppose it's fair to say that I still like my own Graph Explorer for
graphs involving function families with variable parameters.
 
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