I use Python mainly for visualization—creating mathematical animations with Manim and producing graphs for classroom presentations. Though I occasionally use it for computations, its greatest value in my work is bringing mathematical concepts to life through clear and engaging visuals.Cycloidal Curves: Theory, Parametric Equations, and Animation
The purpose of this post is to systematically derive the corresponding parametric equations and implement them in Python for visualization using Manim and Matplotlib. The goal is not only to understand these curves analytically but also to see them come alive through animation.
Cardioid ($r = R$), a special case of the epicycloid.