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:
“Love is a great thing. It is not by chance that in all times and practically among all cultured peoples love in the general sense and the love of a man for his wife are both called love. If love is often cruel or destructive, the reasons lie not in love itself, but in the inequality between people.”
—Anton Pavlovich Chekhov (1860–1904)
“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)
“To say then, the majority are wicked, means no malice, no bad heart in the observer, but, simply that the majority are unripe, and have not yet come to themselves, do not yet know their opinion.”
—Ralph Waldo Emerson (1803–1882)