unit fraction

An unit fractionPlanetmathPlanetmath nd is a fraction whose numerator n=1. If its integer denominator d>1, then a fraction is also a proper fraction. So there is only one unit fraction which is improper, namely 1.

Such fractions are known from Egyptian mathematics where we can find a lot of special representations of the numbers as a sum of an unit fractions, which are now called Egyptian fractionsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath. From the Rhind papyrus as an example:


Many unit fractions are in the pairs of the adjacent fractions. An unit fractions are some successive or non-successive terms of any Farey sequence Fn of a degree n. For example the fractions 12 and 14 are adjacent, but they are not the successive terms in the Farey sequence F5. The fractions 13 and 14 are also adjacent and they are successive terms in the F5.

Title unit fraction
Canonical name UnitFraction
Date of creation 2013-03-22 12:48:25
Last modified on 2013-03-22 12:48:25
Owner XJamRastafire (349)
Last modified by XJamRastafire (349)
Numerical id 10
Author XJamRastafire (349)
Entry type Definition
Classification msc 11A67
Related topic AdjacentFraction
Related topic AnyRationalNumberIsASumOfUnitFractions
Related topic AnyRationalNumberWithOddDenominatorIsASumOfUnitFractionsWithOddDenominators
Related topic UnitFraction
Related topic SierpinskiErdosEgyptianFractionConjecture
Defines Egyptian fraction