Epicycles, complex Fourier series and Homer Simpson’s orbit

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: Mathologer PayPal: (see the Patreon page for details) Today’s video was motivated by an amazing animation of a picture of Homer Simpson being drawn using epicycles. This video is about making sense of the mathematics epicycles. Highlights include the surprising shape of the Moon’s orbit around the Sun, instructions on how you can make your own epicycle drawings, and a crash course of complex Fourier series to make sense of it all. The original Homer epicycle video “Ptolemy and Homer” by Ramiro Serra and Cristián Carman posted on their friend’s Santiago Ginnobili’s YouTube channel can be found here In the video I attribute the animation to Santiago which is a mistake. Also Ramiro told me that unlike what it said in “Ptolemy and Homer“ their animation actually involved 10000 and not just 10