Arithmetic, Geometric, and Harmonic Means

This example dynamically demonstrates the relationships and trends of arithmetic mean, geometric mean, and harmonic mean as variables change, plotted in the same coordinate system. Key mathematical concepts include definitions and properties of these means, and their inequality relationships. Construction highlights the use of GeoGebra commands/objects: Intersect, Point, Segment, Semicircle, Center, OrthogonalLine. Suitable for high school mathematics education to visually understand mean inequalities and their applications.