Once you look beyond the underlying math, its intrigue only increases. Any repeating signal is a super-position of an infinite sine waves with different frequencies and amplitudes. Any signal. A square wave is a sum of infinite sine waves!
I remember spending time in college trying to visualise this, trying to wrap my head around it. And years later, I come across this:
This is the best visualisation of the Fourier Series I’ve come across. Hat tip to Andre Michelle for making this. Have fun playing around with it.