Discovery of Rotational Symmetry in Regular Polygons

This GeoGebra example demonstrates how a regular polygon maintains its shape when rotated about its center, letting learners visually track how corresponding vertices map under successive rotations and thereby identify rotational symmetry and its order. Key concepts include regular polygons, rotational transformations, rotation angle, the uniform distribution of vertices on a circumcircle, and symmetry reasoning based on geometry. Construction overview: Circle is used to define the circumcircle (and its center), Point sets initial vertex locations, Intersect finds new intersection points on the circle to generate the rotated vertices, Polygon connects the computed vertices to form shapes such as poly1 and poly2, and Angle (with parameter α) shows or controls the rotation angle; text/labels (e.g., text1) support explanation. Suitable for middle/high school geometry lessons, classroom demonstrations, and exploratory activities focused on transformations and geometric properties.