The Arithmetic-Logarithmic-Geometric Mean Inequality

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.

The arithmetic-logarithmic-geometric mean inequality states that if then .

[more]

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 .

[less]

Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference: R. B. Nelsen, "Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality," Mathematics Magazine 68(4), 1995 p. 305.



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