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

Loading...
Thumbnail Image
Authors
Northshield, Sam
Issue Date
2011
Type
Article
Language
en_US
Keywords
Research Projects
Organizational Units
Journal Issue
Alternative Title
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.
Description
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
Citation
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
Publisher
American Mathematical Monthly
License
Journal
Volume
Issue
PubMed ID
DOI
ISSN
EISSN