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A triangle wave can be represented as a sum of sine functions through a Fourier series. The key feature is that only the odd harmonics of the base frequency appear in the expansion. Unlike the square wave, where coefficients decrease in proportion to 1/n, the triangle wave’s coefficients decrease much faster, proportional to 1/n². This means that the higher harmonics contribute very little, so the series converges quickly to the actual shape of the triangle wave. As a result, the Fourier approxi
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