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.

Full text available as:

Due to copyright restrictions, this file is not available for public download Click here to request a copy from the OU Author.

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.4169/amer.math.monthly.118.02.130
Google Scholar:	Look up in Google Scholar

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:	0002-9890
Academic Unit/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Related URLs:	http://www.maa.org/pubs/monthly_feb11_to...(Other)
Item ID:	28170
Depositing User:	Ian Short
Date Deposited:	16 Feb 2011 12:00
Last Modified:	03 Dec 2012 15:42
URI:	http://oro.open.ac.uk/id/eprint/28170

Actions (login may be required)

	View Item
RDF+XMLBibTeXRDF+N-TriplesJSONDublin CoreAtomOAI-ORE Resource Map (Atom Format)Simple MetadataReferMETSOAI-ORE Resource Map (RDF Format)HTML CitationASCII CitationMultiline CSVRefMan RIS Format (UTF-8)OpenURL ContextObjectEndNoteMODSOpenURL ContextObject in SpanMPEG-21 DIDLEP3 XMLRefMan RIS FormatRDF+N3Eprints Application Profile	Public: Report issue / request change