Geometric Demonstration of the AM-GM Inequality

This GeoGebra applet provides a visual and geometric demonstration of the Arithmetic Mean-Geometric Mean (AM-GM) inequality. Using geometric objects such as segments, midpoints, circles, and orthogonal lines, it constructs a model that helps users understand the relationship and geometric interpretation between the arithmetic and geometric means. Ideal for teaching and learning inequalities at the high school level and above. By dragging the endpoints of the defining segments, students can observe how the arithmetic mean corresponds to the radius of a semicircle while the geometric mean is represented by a perpendicular chord, making it immediately clear why the arithmetic mean is always greater than or equal to the geometric mean, with equality holding only when the two numbers are identical. This interactive exploration reinforces the conceptual foundation behind one of the most important inequalities in mathematics and supports deeper understanding of optimization, estimation, and proof techniques in algebra and analysis.