A Visual Proof of the Cauchy-Schwarz Inequality in 2D

This illustrates the Cauchy-Schwarz inequality in two dimensions, which states:
.
The gray area on the left is . The same gray area in the right hand image is . For , , hence the inequality.

SNAPSHOTS

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

DETAILS

This image is from S. H. Kung, "Proof without Words: The Cauchy-Schwarz Inequality," Mathematics Magazine, 81(1), 2008 p. 69.
    • 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.