A question that has been bugging me for a while is this:
Say we have $$f_1(x) = \sin(x) $$
If we subtract a third-order sine wave from this sine-wave, of amplitude $1-2/\sqrt{3}$ we get
$$f_2(x) = \sin(x) -(1-2/\sqrt{3})\cdot \sin(3x)$$
If you plot $f_2$, you will see that it is bound by $0.866$.
I am wondering what is so special about the third order harmonic that it can reduce the amplitude of the sine wave. To my knowledge, no other harmonics can do this.
Thanks!