Does algebraic geometry have a good understanding of continued fractions?
What kind of geometric or arithmetic information does a continued fraction expansion contain, if any?
Are there rings of formal continued fractions?
2026-03-29 11:08:24.1774782504
Are continued fractions a mere curiosity?
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As to being "a mere curiosity," I think not, because they are important in KAM theory where "how close to rational" a number is (as measured by its continued fraction expansion) has implications for dynamics. I don't know much about this other than sitting through a couple of expository talks, though.
As for the third question, googling turns up several papers by van der Poorten.