Pi is the infinite ratio between a circle’s circumference and its diameter, but it never repeats and never ends. In this video we see a simple, but visually interesting, example of a complex exponential sum (a two-term Fourier series with incommensurate frequencies) where Pi shows up as one of the angular speeds. The function is: z(θ) = e^(iθ) e^(iπθ) The symbol we write as π ≈ 3.14159 is an irrational number, and its decimal expansion goes on forever without settling into a pattern. When the di