10657
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Arithmetic-Logarithmic-Geometric Mean Inequality
The arithmetic-logarithmic-geometric mean inequality states that if
then
.
Left graphic:
The area under
on the interval
is
.
The area under the tangent at
is
.
Then
.
Right graphic:
The area under
on the interval
is
, as in the left graphic.
The area of the left trapezoid is
.
The area of the right trapezoid is
.
Then
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Rotate and Zoom in 3D
Gamepad Controls
SNAPSHOTS
DETAILS
Reference: R. B. Nelsen, "Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality,"
Mathematics Magazine
68
(4), 1995 p. 305.
PERMANENT CITATION
"
The Arithmetic-Logarithmic-Geometric Mean Inequality
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheArithmeticLogarithmicGeometricMeanInequality/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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 »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
The Arithmetic-Geometric Mean Inequality (I)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
A Visualization of Logarithms
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Arithmetic-Geometric Mean Inequality (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Arithmetic-Geometric Mean Inequality (III)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Napier's Inequality (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Napier's Inequality (I)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Tangent Lines to Exponential and Logarithmic Functions through the Origin
Soledad María Sáez Martínez and Félix Martínez de la Rosa
Hadwiger-Finsler Inequality
Jay Warendorff
Solving Linear Inequalities
Izidor Hafner
Bernoulli Inequality
Chris Boucher
Related Topics
Algebra
Area
Calculus
Exponents and Logarithms
Inequalities
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+