TITLE: Epicycles as precursors of Fourier series
QUESTION [7 upvotes]: How convincing an argument can be formulated to claim that the Ptolemaic epicycles were actually an early precursor of Fourier series? Ptolemy lived ~200AD, and so well pre-dates Fourier ~1800.

REPLY [2 votes]: You might want to take a look at the paper Epicycles are Almost as Good as Trigometric Series by Acosta, Smith, Kosheleva & Kreinovich
They report that epicycles were originally proposed by Appollonius of Perga, late 3rd to early 2nd century BCE, developed by several others, and finalised by Ptolomy in the 1st century AD.
They remark that traditional textbooks term it as 'bad science' that was overthrown by the 'genius' of Copernicus.
But that from the mathematical sense a system of epicycles make perfect sense as a trigonometric series.
They don't comment on any direct connection between epicycles and Fourier series. However, it is known that Fourier was interested in physics - and so likely, astronomy.