Normally I wouldn’t post a sketch to my portfolio site, but I’m proud of this one.
In 2012, I came up with the idea for a simple application to teach Fourier Transforms. The idea was that students could build their own waveforms by messing with the amplitude and phase of the first few terms in the Fourier sequence. For the purposes of the demo, I chose the first six.
In practice, six terms isn’t really enough to get clear shapes, but you can see the beginnings of a few interesting solutions. The triangle wave in particular came out well.
The Fourier Box is still a project I’d like to work on sometime, perhaps as part of a larger Math Education series.
The games included a several number-guessing games which showed the pros and cons of different algorithms, while inviting players to come up with—and try out—algorithms of their own.
The series also included a re-programmable Twenty Questions game, which allowed students to teach the computer about any objects or questions they wished.