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

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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.


Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA



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

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