Anyone who's tried to study mathematics using online resources will have come across these Java applets that demonstrate a particular mathematical idea. Examples:

• http://www.math.ucla.edu/~tao/java/Mobius.html
• http://www.mathcs.org/java/programs/FFT/index.html

I love the idea of this interactive approach because I believe it is very helpful in conveying mathematical principles.

I'd like to create a system for visually designing and publishing these 'mathlets' such that they can be created by teachers with little programming experience.

So in order to create this app, i'll need a GUI and a 'math engine'. I'll probably be working with .NET because thats what I know best and i'd like to start experimenting with F#. Silverlight appeals to me as a presentation framework for this project (im not worried about interoperability right now).

So my questions are:

• does anything like this exist already in full form?
• are there any GUI frameworks for displaying mathematical objects such as graphs & equations?
• are there decent open source libraries that exposes a mathematical framework (Math.NET looks good, just wondering if there is anything else out there)
• is there any existing work on taking mathematical models/demos built with maple/matlab/octave/mathematica etc and publishing them to the web?