If you are remotely interested in mathematics, you'd probably heard of Fourier, or Joseph Fourier . His name comes to mind whenever a physicist, electronic engineer or any technical person deals with frequencies . I don't need to praise Fourier anymore because there are tons of videos and articles about him all over the internet. In this article, I will be talking about Fourier series and epicycles (Foucycle), seemingly two distinct branches of mathematics if you're unaware of Euler's famous formula . Epicycles are essentially circles within circles, they have been studied extensively by astronomers because it was thought planets' motion was perfectly circular (Not to mention how they were convinced the earth was the centre of the universe) until the inverse-square law of planet motion was introduced by Keppler and Newton . Fourier series is essentially a way to approximate any function as the infinite sum of scaled sins and cosines, simple yet revolutionary.