Stern-Brocot Tree

A special type of Binary Tree obtained by starting with the fractions ${\textstyle{0\over 1}}$ and ${\textstyle{1\over 0}}$ and iteratively inserting $(m+m')/(n+n')$ between each two adjacent fractions $m/n$ and $m'/n'$. The result can be arranged in tree form as illustrated above. The Farey Sequence $F_n$ defines a subtree of the Stern-Brocot tree obtained by pruning off unwanted branches (Vardi 1991, Graham et al. 1994).

See also Binary Tree, Farey Sequence, Ford Circle

References

Brocot, A. ``Calcul des rouages par approximation, nouvelle méthode.'' Revue Chonométrique 6, 186-194, 1860.

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, pp. 116-117, 1994.

Stern, M. A. ``Über eine zahlentheoretische Funktion.'' J. reine angew. Math. 55, 193-220, 1858.

Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 253, 1991.