Wolfram Demonstrations Project

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.

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

Contributed by: Chris Boucher

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