The geometry of the trigonometric functions [🎞️ pi.mathematica]

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Ptolemy's Almagest, Book I chapter 11, tabulates every half-degree chord in a circle of diameter 120, and the 1515 printing gives the half-degree chord as 0 31 25 (Wikimedia Commons).

Beautiful: the rotating radius and its projections make sine and cosine feel inevitable. It’s a modern animation of the old chord method—later recast as sine tables in Indian astronomy—and the same circular-motion idea that underlies Fourier analysis.

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