Epitrochoid: Dynamic Construction and Parameter Exploration

This GeoGebra example demonstrates the generation of an epitrochoid, a curve traced by a point attached to a circle rolling externally around a fixed circle. It illustrates how the parametric equations define the curve, with parameters R (radius of fixed circle), r (radius of rolling circle), and d (distance from rolling circle center to the tracing point) controlling the shape. The construction uses the CurveCartesian command to plot the parametric curve, along with Segment and Circle objects to visualize the rolling motion, and sliders (e.g., tmax, d) to animate the process. Text1 displays current parameter values. This is suitable for high school or college students studying parametric equations, coordinate geometry, and dynamic geometry, as well as for exploring mathematical art and curve families.