It’s a shame they only mention Farey when introducing the binary tree construction. It’s called a Stern-Brocot tree (after two independent discoveries). Farey s

It’s a shame they only mention Farey when introducing the binary tree construction. It’s called a Stern-Brocot tree (after two independent discoveries). Farey sequences end up being a specific enumeration over this tree. It’s interesting to see the range of applications this structure has. While it helped me understand a few ideas like how a Cauchy sequence might work, practical applications included things like finding approximate ratios for floating points with various limits on the scale of the denominator and single update list sorting systems that don’t rely on midpoints (they run out of precision and require relabeling rather early). The history of the concept is also worth looking at. A good overview is available in Graham, Knuth, and Patashnik‘s book “Concrete Mathematics.”