The Arithmetic-Geometric Mean Inequality (II)

The arithmetic-geometric mean inequality: , for .
The yellow and green triangles are similar, so . Therefore , , and the figure shows that .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Reference: C. D. Gallant, "Proof without Words: A Truly Geometric Inequality," Mathematics Magazine, 50(2), 1977 p. 98.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.