Robert P. Munafo, 2012 Apr 18.
Two fractions a/b and c/d are adjacent if there is an integer e such that any of the following (equivalent) statements is true:
a/b + 1/e = c/d or c/d + 1/e = a/b
a/b - c/d = 1/e or c/d - a/b = 1/e
a/b - c/d = ±1/e
|a/b - c/d| = 1/e
Similarly, 5/12 minus 3/8 is 1/24, but R2.5/12a and R2.3/8a are not neighbors (R2.2/5a lies between them).
If two fractions are neighboring fractions, then they are also adjacent fractions, but the reverse does not hold true.
For example, R2.1/3a and R2.2/5a are neighbors, and the difference of the internal angles is 1/15. See the neighbors page for an illustrated example of pairs of mu-atoms that are neighbors; you can verify that for each pair of neighbors the two fractions are adjacent. There is a table giving lots of additional examples of pairs of neighbors in the secondary continental mu-atoms article.
revisions: 20010123 oldest on record; 20120416 expand definition and add links; 20120418 reference neighboring fractions
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11