A Short Proof and Generalization of Lagrange's Theorem on Continued Fractions
نویسنده
چکیده
We present a short new proof that the continued fraction of a quadratic irrational eventually repeats. The proof easily generalizes; we construct a large class of functions which, when iterated, must eventually repeat when starting with a quadratic irrational.
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 118 شماره
صفحات -
تاریخ انتشار 2011