Fourier Series, Visualized

[Cassia]

As a keyboardist I have always been fascinated by Additive Synthesis, the approximation of a periodic signal by adding sinewaves. We can see this in action as we start to add sinewaves to get a near square wave by the 4th term. Notice how the amplitude must diminish with each odd and "faster" harmonic. I wish I had visualizations like this when I was in school !!!

[Baruch]

Ptolemy's epicycles were an early version.  Copernicus' actual system, though heliocentric, had more epicycles than Ptolemy.  It was only with Kepler that this fact could be hidden, for awhile.  Only to be rediscovered in the heat equation studies of Fourier.

[Cassia]

And then there is the ancient Greek Antikythera mechanism (that may be as old as 200BC) that just bypasses all the complex math to solve astronomical positioning

[Baruch]

And then there is the ancient Greek Antikythera mechanism (that may be as old as 200BC) that just bypasses all the complex math to solve astronomical positioning

Genius analog computer.  Devised by Archimedes?