Hypotrochoid (Inner Trochoid) Drawn via Parametric Intersection and Locus

This GeoGebra example demonstrates how a hypotrochoid (inner trochoid) can be visualized as a smooth, often closed curve generated from the interplay of circular motion and parameter-controlled geometry. It centers on parameterized curves and the role of trigonometric functions in producing coordinates over time, along with the geometric meaning of radius ratios and offsets between the generating circles. Construction-wise, it uses Intersect to compute key intersection points of the involved geometric objects, and then applies Locus to trace the path of the selected point as parameters evolve. The construction relies on parameters such as d, b, α, a, q, p, P, c, and coordinate variables tx, ty (from the provided construction summary) to control the curve’s shape. Suitable for advanced secondary education, pre-university, and introductory undergraduate geometry/dynamics visualization, especially for lessons on parametric equations, trigonometric curve generation, and locus-based construction.