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.
Contributed by:
Chris Boucher
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This image is from S. H. Kung, "Proof without Words: The Cauchy-Schwarz Inequality,"
Mathematics Magazine
,
81
(1), 2008 p. 69.
Cauchy's Inequality
(
Wolfram
MathWorld
)
"
A Visual Proof of the Cauchy-Schwarz Inequality in 2D
" from
The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AVisualProofOfTheCauchySchwarzInequalityIn2D/
Contributed by:
Chris Boucher
College Mathematics
Plane Geometry
Vector Algebra
The Cauchy-Schwarz Inequality for Vectors in the Plane
Gram-Schmidt Process in Two Dimensions
Shortest Distance between a Point and a Line in 2D
2D Vector Addition
Vector Addition in a Plane
QR Decomposition
The Triangle Inequality
The Erdös-Mordell Inequality
Understanding 2D Translation
Understanding 2D Shearing
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