What is an epicycle? How is it important in Ptolemy's explanation of the retrograde motions of the planets?
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Fourier epicycles are a fascinating visual interpretation of how complex shapes and signals can be represented as sums of simple circular motions. The idea originates from Fourier series, which express any periodic function as the sum of sine and cosine waves of varying frequencies, amplitudes, and phases. In the epicycle visualization, each sine and cosine component becomes a rotating circle (an “epicycle”) whose motion contributes to the overall path traced by the endpoint of the last circle i
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