The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle approximation "without" recourse to calculus. Rather charmingly, our approach exploits the motion of the pendulum to visualise the process of taking an important limit and can be used to explore the meaning of mathematical approximation in physical systems.