Stern–Brocot Tree

Abstract

Christoffel words have a strong connection with continued fractions of rational numbers, as was recognized by Christoffel. They are in some sense equivalent to them, being a way to encode the expansion of these numbers into continued fractions. The Stern–Brocot tree is another way to compute continued fractions. Among other things in this chapter, equivalence is shown between semi-convergents of rational numbers, nodes in the Stern–Brocot tree, palindromic prefixes of centralwords, points on the frontier of the convex hull of some subset of Z2 associatedwith a rational number, and special points relative to a half-line of rational slope.