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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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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
Mathematics, Computing and Technology
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Item ID: 28170
Depositing User: Ian Short
Date Deposited: 16 Feb 2011 12:00
Last Modified: 25 Feb 2016 17:40
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