  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.
