The Inequality of Arithmetic and Geometric Means from Multiple Perspectives

  • The Inequality of Arithmetic and Geometric Means from Multiple Perspectives

    Richard Askey, Ryota Matsuura, and Sarah Sword
    Given three numbers a, b, and c, we can find their mean (or average) as (a + b + c)/3. More precisely, this expression yields the arithmetic mean of a, b, and c. A different kind of mean, however, uses the product of these numbers instead of their sum. It is called the geometric mean and is given by the expression (abc)1/3. We may interpret the geometric mean of nonnegative a, b, and c as the side length of a cube whose volume is the same as that of a right rectangular prism with dimensions a, b, and c.
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