The Stern–Brocot tree, and the Stern–Brocot sequences of order i for i = 1, 2, 3, 4 In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was introduced independently by Moritz Stern (1858) and Achille Br