The inequality of arithmetic and geometric means from multiple perspectives

• Autores: Richard Askey, Ryota Matsuura, Sarah Sword, Brian M. Dean (ed. lit.), Daniel Ness (ed. lit.), Nick Wasserman (ed. lit.)
• Localización: Mathematics teacher, ISSN-e 2330-0582, ISSN 0025-5769, Vol. 109, Nº 4, 2015, págs. 314-318
• Idioma: inglés
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• Resumen

  • 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.