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:
“The doctrine of equality!... But there exists no more poisonous poison: for it seems to be preached by justice itself, while it is the end of justice.... “Equality for equals, inequality for unequals”Mthat would be the true voice of justice: and, what follows from it, “Never make equal what is unequal.””
—Friedrich Nietzsche (1844–1900)
“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)
“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)
“The aim of every artist is to arrest motion, which is life, by artificial means and hold it fixed so that a hundred years later, when a stranger looks at it, it moves again since it is life. Since man is mortal, the only immortality possible for him is to leave something behind him that is immortal since it will always move. This is the artist’s way of scribbling “Kilroy was here” on the wall of the final and irrevocable oblivion through which he must someday pass.”
—William Faulkner (1897–1962)