Dynamic Construction of Regular Polygons

This GeoGebra example dynamically constructs regular polygons with variable numbers of sides, illustrating their symmetry, angular properties, and area behavior. Core mathematical concepts include planar geometry, rotational transformations, the relationship between circles and polygons, and limit processes where increasing side count approximates a circle. Construction utilizes GeoGebra commands such as Circle, Rotate, Polygon, Segment, and Midpoint, with key parameters n (number of sides) and r (radius) driving the model. The activity is suitable for middle to high school geometry classes and can bridge into calculus introductions on limits and area approximation. It enables teachers to demonstrate symmetry and area convergence, while students interact with parameters to explore continuous shape changes.