Four Color Theorem: Coloring Polygonal Regions

① This GeoGebra example demonstrates the Four Color Theorem by constructing a planar map composed of multiple polygonal regions and coloring them so that adjacent regions have different colors, using at most four colors. ② The core mathematical concept is the Four Color Theorem from graph theory, involving planar graph coloring, adjacency relations, and chromatic number. ③ Construction details: Based on the summary, the example uses the Polygon command to create several polygons (poly1 to poly5), Point objects for vertices (A to N), and Segment commands for edges (a to l), forming nested or adjacent regions. Each polygon is assigned a distinct color to verify the theorem's condition. ④ Suitable for high school to early university students, this example serves as an interactive tool for exploring graph theory, map coloring, and algorithmic thinking, and can be used by teachers to illustrate the theorem in mathematics or computer science classes.