Here is a project I did a while ago which is one of those that came to a certain point, then something else popped in and dust started settling on them.
Somehow I stumbled across X3 Mathematical Methods. It's some math course material, unfortunately completely out of context, but the animated gif caught my eye (of course I am talking about the animation on the right side). Like Pawlov's Dog I immediately thought "If it moves it can be done in Flash".
Well, this thing looks pretty easy to build and one could think that it is even possible to do this in keyframe animation. And for actionscripting? Well there is this easy formula at the top - let's plug it in...
A few hours later I had to admit that this task was more complex than expected. The reason is that this is based on so called "Complex Numbers" which is a branch of Mathematics that deals with the "Dark Side" or something that you would write in Flash Math.sqrt(-1). Unfortunately this was nothing they taught me in school. So I tried to approach this problem from the classical trigonometrical side.
And I got pretty far - to the point where I found out that the secret lies in the radius of the inner circle. Now I asked Oliver Kerr who is responsible for this course for a tip. And indeed he sent me a formula almost instantly. Unfortunately it dealt with complex numbers again, but I was able to tweak it into Marioland Mathematics and wow - it worked!
Almost. Somehow there are cases when the program does not find a suitable solution. I did not find out why, my guess is that it is caused by non-exact internal calculations, but it might be a simple stupid eror by myself.
I made this into a little menu which you can find on Transnational Republic.