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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.
RELATED LINKS
Arithmetic Mean
(
Wolfram
MathWorld
)
Geometric Mean
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
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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