Regular Star Polygon Construction and Dynamic Demonstration

This GeoGebra example demonstrates how to construct regular star polygons by equally dividing points on a circumcircle and connecting them with a fixed step size. Core mathematical concepts include regular polygons, greatest common divisor (GCD/HCF), modular arithmetic, equally spaced points on a circle, and the density and connectivity of star polygons. The construction uses Circle to create the circumcircle, Point to establish the initial vertex, Sequence to generate the vertex list, PolyLine to connect vertices in order, GCD to compute the greatest common divisor of the step size and vertex count, and Polygon to form the closed figure. Sliders (box1, box2, box3), text labels (text1, text2, text3), and opacity controls enable dynamic parameter adjustment. Suitable for high school geometry electives, university discrete mathematics, or computer graphics introductory courses, and ideal for classroom demonstrations and student exploration of star polygon construction rules.