Displaying similar documents to “Infinite product representations in complex quadratic fields”

An objective and practical method for describing and understanding ratios

D. H. Fowler (1993)

Mathématiques et Sciences Humaines

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This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.

Discrete planes, ℤ 2 -actions, Jacobi-Perron algorithm and substitutions

Pierre Arnoux, Valérie Berthé, Shunji Ito (2002)

Annales de l’institut Fourier

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We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a ℤ 2 -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of ℤ 2 -actions by rotations.