In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. Other positive integers are impolite. Polite numbers have also been called staircase numbers because the Young diagrams representing graphically the partitions of a polite number into consecutive integers (in the French style of drawing these diagrams) resemble staircases. If all numbers in the sum are strictly greater than one, the numbers so formed are also called trapezoidal numbers because they represent patterns of points arranged in a trapezoid.
The problem of representing numbers as sums of consecutive integers and of counting the number of representations of this type has been studied by Sylvester, Mason, and Leveque, as well as by many other more recent authors.
Read more about Polite Number: Examples and Characterization, Politeness, Construction of Polite Representations From Odd Divisors, Trapezoidal Numbers
Famous quotes containing the words polite and/or number:
“... the movie woman’s world is designed to remind us that a woman may live in a mansion, an apartment, or a yurt, but it’s all the same thing because what she really lives in is the body of a woman, and that body is allowed to occupy space only according to the dictates of polite society.”
—Jeanine Basinger (b. 1936)
“I can’t quite define my aversion to asking questions of strangers. From snatches of family battles which I have heard drifting up from railway stations and street corners, I gather that there are a great many men who share my dislike for it, as well as an equal number of women who ... believe it to be the solution to most of this world’s problems.”
—Robert Benchley (1889–1945)