A straight line (y=x) can be written as a sum over sinusoids, known as a Fourier Series.pic.twitter.com/Obii1qd62T
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Yes, but the animation also clearly seems to indicate that the series does not converge to the white line, exactly due to this condition.
i don't see what you're talking about.. the line passes directly through (0,0)
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...ah, whoops. Nevermind me, I did not see that x-axis does not start at 0 in your animation. Sorry.
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The important observation here is that there is pointwise convergence, but not uniform convergence. This can be seen in the "Gibbs phenomenon" at the corners (at the left and right edges of the figure above). For more: https://en.wikipedia.org/wiki/Gibbs_phenomenon …
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