Self-intersection points of an Epitrochoid via polyline approximation (GeoGebra)

This example demonstrates how to locate self-intersection points of an Epitrochoid by approximating the smooth parametric curve with a polyline (piecewise linear) discretization, then computing intersections between polyline segments. The key mathematics includes parametric curve graphing, discretization/approximation (polyline method), generating parameter sample sets, and using intersection computations to extract self-crossing points. Construction in GeoGebra uses Textfield and LaTeX for formula and label display; CurveCartesian to build the curve expression in Cartesian coordinates; Sequence together with Mod/Div to generate and control the parameter sampling (including periodic behavior); PolyLine to form two sets of polyline segments (e.g., poly1a and poly2a) from sampled points; and Intersect to compute the intersection locations representing the curve’s self-intersection points. It is suitable for secondary to early university learners studying coordinate geometry, parametric equations, and computational geometry/visual math workflows.