Lessons taught; Lessons learnt

Terminology

I've been wondering for a while what to call the little visualisations that I generate from time to time. I've seen quite a few terms used on different sites: interactivities, applets, worksheets, animations, miniworlds, interactive environments, etc. Now I can add another one: mathlets. I wish we could just pick one term and stick to it. For the rest of this post I'll refer to them as gromits.

Links

Elisha Peterson has created a number of interesting Geogebra gromits which are worth exploring, as well as a nicely written tutorial explaining how to generate an interactive Cobweb Diagram using Geogebra.

The Tools section of the Geogebra wiki is slowly building up a decent collection of Geogebra tools. The Tetris tools are particularly fun!

Splines

On the topic of tools, and following on from my earlier post on curves and splines, here's a Geogebra tool which implements a Catmull-Rom spline: cr-spline.ggt. Example gromit:

Frustrations

I've been trying to delve into some of the new matrix capabilities of Geogebra 3.2, and I'm getting quite frustrated! They don't seem to be particularly well integrated into the rest of the system -- for example, I've been trying for about 30 minutes now to figure out how to 'extract' the number from a 1x1 matrix (represented by, for example {{-4}}), so that I can calculate with matrices and display the results. Element[] would be the obvious tool, but it just returns 'undefined'.

A confession — I knew very little about the theory of splines before writing this week’s introduction to Bezier curves and splines. I’ve been trying to do some catch-up reading in the last few days, and have found quite a few interesting links I thought I should share:

• The Algorithmist has a very interesting series of articles on the history, theory, and calculation of splines. They are well explained and easy to read.
• Tim Lambert has an interesting page giving interactive examples of many different splines: the natural cubic spline, Bezier splines, B-splines and Catmull-Rom splines. Very interestingly for me, he gives the source code for the interactive Java applets — something for me to read through over the weekend!
• Grady Wright also has an interesting interactive applet demonstrating cubic splines.
• It shouldn’t come as a surprise that Mathematica has excellent integrated support for splines — see the “Splines” entry at Mathworld for links to the Mathematica routines. If only I had a spare grand for a copy of it!

If you know any other good resources on the theory or calculation of splines, then please leave a comment. Any recommendations for books on this area would also be appreciated — I need something to keep me occupied this summer…