Inequality of Arithmetic and Geometric Means

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

Read more about Inequality Of Arithmetic And Geometric Means:  Background, The Inequality, Geometric Interpretation, Example Application, Proofs of The AM–GM Inequality

Famous quotes containing the words inequality, arithmetic, geometric and/or means:

    Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom.
    Francis Picabia (1878–1953)

    O! O! another stroke! that makes the third.
    He stabs me to the heart against my wish.
    If that be so, thy state of health is poor;
    But thine arithmetic is quite correct.
    —A.E. (Alfred Edward)

    In mathematics he was greater
    Than Tycho Brahe, or Erra Pater:
    For he, by geometric scale,
    Could take the size of pots of ale;
    Resolve, by sines and tangents straight,
    If bread and butter wanted weight;
    And wisely tell what hour o’ th’ day
    The clock doth strike, by algebra.
    Samuel Butler (1612–1680)

    I concluded that I was skilled, however poorly, at only one thing: marriage. And so I set about the business of selling myself and two children to some unsuspecting man who might think me a desirable second-hand mate, a man of good means and disposition willing to support another man’s children in some semblance of the style to which they were accustomed. My heart was not in the chase, but I was tired and there was no alternative. I could not afford freedom.
    Barbara Howar (b. 1934)