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Ford circles, continued fractions, and rational approximation

Short, Ian (2011). Ford circles, continued fractions, and rational approximation. American Mathematical Monthly, 118(2) pp. 130–135.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.4169/amer.math.monthly.118.02.130
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Abstract

We give an elementary geometric proof using Ford circles of a well-known theorem of Lagrange, which says that the convergents of the continued fraction expansion of a real number α coincide with the rationals that are best approximations of α.

Item Type: Journal Article
Copyright Holders: 2011 The Mathematical Association of America
ISSN: 1930-0972
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Related URLs:
Item ID: 28170
Depositing User: Ian Short
Date Deposited: 16 Feb 2011 12:00
Last Modified: 27 Apr 2014 05:23
URI: http://oro.open.ac.uk/id/eprint/28170
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