HackerBut what is a Fourier series? From heat flow to drawing with circles | DE4
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Treat a traced drawing as a complex position over time. Rotate into one component’s frame and average over a full period: that component stands still while the other integer rotations cancel.
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But each of these vectors just makes a whole number of rotations around 0, so its average value as t ranges from 0 to 1 will be 0.So taking the average of this modified function is a clever way to kill all the terms other than c2.