Geometric Mean 2.1: Dynamic Inequality Visualization

①This GeoGebra example dynamically demonstrates the relationship between the geometric mean (gm) and arithmetic mean (am) of two positive numbers a and b, visually confirming the classic inequality that the geometric mean is less than or equal to the arithmetic mean. ②Core mathematical concepts include geometric mean, arithmetic mean, inequalities, and comparisons with polynomial and power functions, with additional context from tangent functions and stochastic processes. ③Construction highlights: objects a and b serve as adjustable parameters, am and gm are computed, and text1/text2 display numerical values and the inequality; the graphical representation may include function plots or geometric constructions to aid understanding. ④Suitable for high school and above, this example is ideal for teaching algebra-geometry connections, inequality proofs, and as a preparatory tool for calculus or statistics.