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A short proof and generalization of Lagrange's theorem on continued fractions

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2011
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SUNY Plattsburgh Mathematics Faculty Work
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http://hdl.handle.net/20.500.12648/1111
Abstract
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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Northshield, S. (2011). A short proof and generalization of Lagrange's theorem on continued fractions. American Mathematical Monthly, 118(2). http://doi.org/10.4169/amer.math.monthly.118.02.171
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This article has been published in the February 2011 issue of American Mathematical Monthly, published by Taylor & Francis, Ltd. on behalf of the Mathematical Association of America: http://www.jstor.org/stable/10.4169/amermathmont.118.issue-2
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