Toot

Written by Leon P Smith on 2024-09-30 at 14:33

@boarders @acowley

You might try solving Project Euler #192, that's the exact problem that helped spawn the insights that lead to all of this.

I mean, at first I had no idea how to even approach the problem, but somehow I stumbled into the answer, realized that the answer wasn't really that difficult, and was shocked how few people managed to solve that problem successfully.

At that point it was obvious that continued fractions were an underappreciated thing... I don't know how long I spent fumbling with them fruitlessly as an undergrad, but I made several efforts. "The Higher Arithemetic", which Wiles considers his favorite introduction to number theory (mentioned in the preface to the 6th edition of Hardy and Wright), has an explanation that might have clicked had I saw it as an undergrad, as it's morally the same explanation as the one I remember seeing on cut-the-knot.

So yeah, there's something that's definitely a non-obvious leap, but once you know how to use a tiny bit of linear algebra to make that leap, it somehow seems manageable, even if it's something nobody is likely to find for themselves. Thus part of the reason to make the Stern-Brocot tree the frontispiece.

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