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:

    However energetically society in general may strive to make all the citizens equal and alike, the personal pride of each individual will always make him try to escape from the common level, and he will form some inequality somewhere to his own profit.
    Alexis de Tocqueville (1805–1859)

    Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.
    Ralph Waldo Emerson (1803–1882)

    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)

    Conspicuous consumption of valuable goods is a means of reputability to the gentleman of leisure.
    Thorstein Veblen (1857–1929)