Homothetic Polygons in a Circle: Rotation and Mirror Construction

This GeoGebra example demonstrates the generation of a series of homothetic (similar) polygons inside a circle, dynamically transformed through rotation and mirror operations. The core mathematical concepts include homothety (scaling about a center), similarity of polygons, circle geometry, rotational symmetry, and reflection. The construction uses commands such as Sequence to create polygon lists, Polygon for the base shape, Mirror and Rotate for transformations, Circle for the circumcircle, Midpoint for the center, and If for conditional logic. Sliders (e.g., k, kk) control the homothety ratio and rotation angle, allowing interactive exploration. Suitable for high school and undergraduate students studying geometric transformations, similarity, and dynamic geometry, as well as for teachers demonstrating composite transformations in a visual environment.