I had more to say on this, but after being obsessed for a week I don't seem to be returning to it, so will just link a couple more things:
• The treatment in Concrete Mathematics, pp. 116–123 and exercises
• This video by Wildberger: youtube.com/watch?v=qPeD87HJ0U

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"Continued Fractions without Tears" — this nice 1981 article maa.org/programs/maa-awards/wr was pointed to me by Python developer Mark Dickinson (on a Stack Overflow comment; I don't know him otherwise) — it's a great read, motivates/develops continued fractions from first principles.

David Bellos mentions 3 ways to avoid translation:
• “Just” get everyone to speak the same language (Romans, …)
• “Just” ignore other languages (Edo Japan, Albania)
• “Just” learn each other's languages (India)
— historically it was in fact the norm to do without translation.

The phrase "nth cousin m times removed" means that if the (least) distances to a common ancestor are d1 and d2, then min(d1, d2) = n+1, and |d1 - d2| = m.

(Usual "cousin" with d1=d2=2 are n=1, m=0.)

(Just noting down for future reference, though I don't expect to ever use it…)

“Very often research which has deeply interested me while I was investigating it loses its interest for me just after I have the solution, unhappily at a time which coincides with the period when I have to record it.”
— Hadamard (1949?)

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