Inequality of Arithmetic and Geometric Means/proofs of The Am-gm Inequality

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

    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)

    I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
    Gottlob Frege (1848–1925)

    New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.
    Roland Barthes (1915–1980)

    I want a revamped feminism. Putting the vamp back means the lady must be a tramp. My generation of the Sixties rebels wanted to smash the bourgeois codes that had become authoritarian totems of the Fifties.... Thirty years later, we’re still stuck with the [”nice” girl].
    Camille Paglia (b. 1947)

    Trifles light as air
    Are to the jealous confirmation strong
    As proofs of holy writ.
    William Shakespeare (1564–1616)