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Proof without words of the AM–GM inequality: PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. Visual proof that (x + y) 2 ≥ 4xy. Taking square roots and dividing by two gives the AM ...
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In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then
Proof without words of the inequality of arithmetic and geometric means, drawn by CMG Lee. PR is a diameter of a circle centred on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, right triangle PGR can be split into two similar triangles PQG and GQR; GQ / a = b / GQ, hence GQ = √(ab), the geometric mean ...
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The outhouse is a unit of area used in nuclear physics equal to 10 −6 barns (100 am 2 = 10 −34 m 2). The barn (b) is a unit of area used in nuclear physics equal to one hundred femtometres squared (100 fm 2 = 10 −28 m 2). The are (a) is a unit of area equal to 100 m 2. The decare (daa) is a unit of area equal to 1000 m 2.