Explore the fascinating world of epicycles, complex Fourier series, and their connection to Homer Simpson's orbit in this 26-minute video. Dive into the mathematics behind epicycles, starting with the surprising shape of the Moon's orbit around the Sun. Learn how to create your own epicycle drawings and gain a crash course in complex Fourier series to understand the underlying principles. Discover the link between these mathematical concepts and real-world applications, including an amazing animation of Homer Simpson being drawn using epicycles. Follow along as the video breaks down the mathematics, provides practical examples, and offers insights into the historical and modern significance of these concepts in various fields.