Theorem of Geometric Mean

This GeoGebra example demonstrates the Theorem of Geometric Mean through interactive geometric constructions, illustrating how to prove the geometric mean inequality using visual methods, often applied to triangles or polygons. Key mathematical concepts include geometric mean, geometry, angles, geometric transformations, and inequality theory. Construction highlights: it employs the Rotate command for rotational symmetry, Angle command for angle definition and measurement, Segment command to draw line segments, Polygon command to form polygons, and Point command to label critical vertices; objects include multiple points (e.g., A_1, B_1, P), segments, polygons, text labels (text1 to text11), and parameters (α_1, f_1) to enable dynamic exploration. Suitable for high school or university mathematics courses, particularly in geometry, algebraic inequalities, or math competition training, to provide an intuitive grasp of abstract theorems.