Farey Addition

Robert P. Munafo, 2009 May 10.

An operation performed on two rational numbers (expressed as reduced fractions) in which you add the numerators together and add the denominators together (or, as your children might say, adding fractions the way you always wanted to!).

The result of a Farey addition is always somewhere between the two original fractions.

If the two original fractions have no fraction between them with a smaller denominator (example: 1/3 and 1/2) then the result of the Farey addition is the fraction with smallest denominator between them (in this example, 2/5).

If the two original fractions are the internal angles (that is, they are each reduced fractions, see relatively prime) of two mu-atoms, then Farey addition gives the internal angle of the inner neighbor of those two mu-atoms.

See also smaller neighbor, larger neighbor.


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index
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