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

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This illustrates the Cauchy-Schwarz inequality in two dimensions, which states:

[more]

.

The gray area on the left is . The same gray area in the right hand image is . For , , hence the inequality.

[less]

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


Snapshots


Details

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



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send