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The Arithmetic-Geometric Mean Inequality (II)

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The arithmetic-geometric mean inequality: , for .

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The yellow and green triangles are similar, so . Therefore , , and the figure shows that .

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

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Reference: C. D. Gallant, "Proof without Words: A Truly Geometric Inequality," Mathematics Magazine, 50(2), 1977 p. 98.

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