Egyptian Fraction

An Egyptian fraction is the sum of distinct unit fractions, such as . That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number a/b; for instance the Egyptian fraction above sums to 43/48. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including 2/3 and 3/4 as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics.

Read more about Egyptian Fraction:  Ancient Egypt, Medieval Mathematics, Modern Number Theory, Open Problems

Famous quotes containing the words egyptian and/or fraction:

What greater light can be hoped for in the moral sciences? The subject part of mankind in most places might, instead thereof, with Egyptian bondage expect Egyptian darkness, were not the candle of the Lord set up by himself in men’s minds, which it is impossible for the breath or power of man wholly to extinguish.
John Locke (1632–1704)

The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.
Charlotte Perkins Gilman (1860–1935)