The AM–GM Inequality

Averages and products

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• AM–GM: $\frac{a + b}{2} \ge \sqrt{ab}$, with equality when $a = b$.
• A semicircle shows it: a half-chord never exceeds the radius.
• Fixed sum → product is largest when the parts are equal.

Steps

1. A picture proof
2. Four rectangles in a square
3. The best rectangle
4. A number plus its reciprocal
5. Three numbers
6. Biggest product
7. Fencing by a river