But what is a Fourier series? From heat flow to drawing with circles | DE4

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把一笔画看成随时间变化的复数位置。要取出一个旋转分量，就转入它的参考系再对完整周期求平均：它停住，其余整圈旋转的分量相互抵消。

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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.