The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers such that
Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction. Engel expansions are named after Friedrich Engel, who studied them in 1913.
An expansion analogous to an Engel expansion, in which alternating terms are negative, is called a Pierce expansion.
Read more about Engel Expansion: Engel Expansions, Continued Fractions, and Fibonacci, Algorithm For Computing Engel Expansions, Example, Engel Expansions of Rational Numbers, Engel Expansions For Some Well-known Constants, Growth Rate of The Expansion Terms
Famous quotes containing the words engel and/or expansion:
“Now folks, I hereby declare the first church of Tombstone, which ain’t got no name yet or no preacher either, officially dedicated. Now I don’t pretend to be no preacher, but I’ve read the Good Book from cover to cover and back again, and I nary found one word agin dancin’. So we’ll commence by havin’ a dad blasted good dance.”
—Samuel G. Engel (1904–1984)
“The fundamental steps of expansion that will open a person, over time, to the full flowering of his or her individuality are the same for both genders. But men and women are rarely in the same place struggling with the same questions at the same age.”
—Gail Sheehy (20th century)