Rolling a Regular Polygon: Vertex Trajectories and Animation

① This example demonstrates a regular polygon (e.g., equilateral triangle, square) rolling without slipping along a horizontal line, showing the path traced by its vertices and animating the entire rolling process. ② Core mathematical concepts include rigid-body rotation, composition of translation and rotation, geometric properties of regular polygons, periodicity of vertex trajectories, and generation of cycloid-like curves. ③ Construction highlights: using GeoGebra commands such as Rotate to rotate the polygon about a vertex, Polygon to create the regular polygon, LineBisector and Intersect to determine rotation centers and contact points, Sequence to generate vertex lists, sliders to control the number of sides n, side length, and number of turns, buttons to trigger animation, and lists to store trajectory points. ④ Suitable for upper secondary to early university students, this is ideal for understanding rotational symmetry, parametric curves, and dynamic geometry, and can serve as material for mathematical experiments or inquiry-based learning.