The Calkin–Wilf tree contains every positive rational number exactly once.

Each vertex *a/b* has two children: *(a+b)/b* and *a/(a+b)*.

Traversing the tree breadth-first results in the Calkin–Wilf sequence, depicted by the spiral below.

- Calkin–Wilf tree on Wikipedia.
- Recounting the Rationals, the original paper by Neil Calkin and Herbert Wilf.
- Recounting the Rationals, part I: a series of expository blog posts about the original paper on The Math Less Traveled. Highly recommended!
- Fractions on a Binary Tree II by A. Bogomolny.
- Enumerating the Rationals: some remarkable properties of the Calkin–Wilf sequence.