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The Arithmetic-Geometric Mean Inequality (II)


	The arithmetic-geometric mean inequality: , for . The yellow and green triangles are similar, so . Therefore , , and the figure shows that .


	Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
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Reference: C. D. Gallant, "Proof without Words: A Truly Geometric Inequality," Mathematics Magazine, 50(2), 1977 p. 98.

Arithmetic Mean (Wolfram MathWorld)

Geometric Mean (Wolfram MathWorld)

"The Arithmetic-Geometric Mean Inequality (II)" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheArithmeticGeometricMeanInequalityII/

Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa

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