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Abstract

The article begins by associating a certain graph, which the author calls a hidden graph, to the plane lattice points visible from the origin. Via several transformations it is rendered in different geometric forms, called Farey tail, Farey comb, Farey eye and symmetrical Farey eye; the classical Farey fractions appear. Then, best rational approximations to real numbers are introduced, as well as continued fractions. There is also a discussion of Hurwitz chains and of algorithms generating various expansions into continued fractions, which constitutes the largest part of the text. The article contains lots of interesting material. Reading it will require some patience from the reader, as no result is distinguished or highlighted (as substantial or interesting), and neither does the author give at the beginning any hint or overview as to the content of his text

Topics: 1. J. Goldman, Hurwitz sequences, the Farey process and general continued fractions, Adv. in
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.359.9944
Provided by: CiteSeerX
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