It is well known that the shadow of the tip of a rotating rod traces out a sine wave:

**SINEWAVE**

It’s also well known that the Fourier components of a **square wave** are:

So consider a rotating arm, of length 1 and rotation rate 1. On the arm a hand of length 1/3 rotates at a rate of 3. On the hand a finger of length 1/5 rotates at a rate of 5… and so on.

Question: What path in space will the tip of the set of rotating arms trace out?

**SQUARE WAVE**

The Fourier components of a **sawtooth wave** are:

**SAWTOOTH WAVE**

And here is a full wave rectified sinewave:

**RECTIFIED SINEWAVE**