An arborist's guide to the rationals
  There are two well-known ways to enumerate the positive rational numbers in an infinite binary tree: the Farey/Stern-Brocot tree and the Calkin-Wilf tree. In this brief note, we describe these two trees as `transpose shadows' of a tree of matrices (a result due to Backhouse and Ferreira) via a new proof using yet another famous tree of rationals: the topograph of Conway and Fung. 
Katherine E. Stange
math.NT math.CO