This is my inverse kinematics solver for a BYU class project. I wrote it in C++ and used OpenGL for the graphics. The video is short, but it is a good way to show what the solver is doing.
With ordinary forward kinematics, I choose the joint angles and work out where the end of the chain goes. Inverse kinematics asks the question in the other direction: where should the joints go if I want the end to reach a particular target?
The on-screen chain makes that relationship much easier to think about than a page full of angles. It is the same general kind of problem that comes up in articulated characters and robot arms. I like assignments where the math turns into something visible enough that I can play with it.