Roullete curves, coin paradox and Aristotle's wheel paradox

Abstract

This work discusses the concept of roulette, the generated curves that occur when one curve rolls without slipping along another, tracing the path of a fixed point. The coin paradox and Aristotle's wheel paradox are used as pedagogical motivations to discuss the parametric equations of epicycloids and hypocycloids, providing a geometrical intuition for the mathematical derivations and computational implementation of those curves. Python code is provided to motivate the application of the derived parametric equations, resulting in concrete visualizations and animations.