Central Angle Exploration: Relationship to Regular Polygon Sides

This GeoGebra example dynamically explores how the central angle (the angle subtended by each side at the center) of a regular polygon depends on the number of sides. The core mathematical concepts include regular polygon symmetry, the relationship between central and inscribed angles, and the pattern of angle change as the side count increases. The construction uses commands such as Circle to create the circumcircle, Segment and Rotate to generate polygon edges, Angle to measure the central angle α, and a slider n to control the number of sides. Additional tools like Polygon, Ray, Midpoint, Intersect, LineBisector, and Mirror are employed to build auxiliary lines, angle bisectors, and symmetric figures, visually demonstrating that as n grows, the central angle decreases and approaches 0°. This resource is suitable for middle school to high school geometry lessons, classroom demonstrations, or student self-exploration, and can also serve as an intuitive introduction to the concept of limits.