adjacent fraction
Two fractions and , of the positive integers are adjacent if their difference is some unit fraction , that is, if we can write:
For example the two proper fractions and unit fractions and are adjacent since:
and are not since:
It is not necessary of course that fractions are both proper fractions:
or unit fractions:
All successive terms of some Farey sequence of a degree are always adjacent fractions. In the first Farey sequence of a degree 1 there are only two adjacent fractions, namely and .
Adjacent unit fractions can be parts of many Egyptian fractions:
Title | adjacent fraction |
---|---|
Canonical name | AdjacentFraction |
Date of creation | 2013-03-22 12:48:23 |
Last modified on | 2013-03-22 12:48:23 |
Owner | XJamRastafire (349) |
Last modified by | XJamRastafire (349) |
Numerical id | 17 |
Author | XJamRastafire (349) |
Entry type | Definition |
Classification | msc 11A67 |
Related topic | FareySequence |
Related topic | UnitFraction |
Related topic | ContinuedFraction |
Related topic | NumeratorAndDenominatorIncreasedBySameAmount |