Simulation of a Rolling Polygon

This example demonstrates the dynamic process of a polygon rolling along a straight line. Using GeoGebra rotation, centroid, and polygon commands, it accurately simulates the geometric transformations that occur as an arbitrary polygon rolls. The applet allows users to adjust the shape and size of the polygon, observe each rotation step as the polygon pivots around successive vertices on the line, and trace the paths generated by selected points during the rolling motion. Combined with integral calculus and coordinate geometry, the applet explores the locus of relevant points—such as vertices, the centroid, and other marked positions—as well as the area swept out by the rolling polygon over one or multiple full rotations. This makes it an intuitive teaching tool for understanding rigid-body planar motion and the practical applications of calculus. Students can visually connect abstract concepts like parametric curves, arc length, and area integration to concrete geometric motion. The interactive nature of the applet encourages exploration: learners can experiment with different polygons, observe how symmetry affects the trajectory of points, and verify theoretical predictions through dynamic visualization. By watching the traced curves emerge in real time, students gain deeper insight into the relationship between discrete rotations and continuous motion, bridging the gap between classical geometry and analytical methods.