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There are two well-known ways to enumerate the positive rational numbers inan 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 atree of matrices (a result due to Backhouse and Ferreira) via a new proof usingyet another famous tree of rationals: the topograph of Conway and Fung.

An arborist's guide to the rationals