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Other Generalizations of Continued Fractions

  • Oleg Karpenkov
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Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 26)

Abstract

In this chapter we present some other generalizations of regular continued fractions to the multidimensional case. The main goal for us here is to give different geometric constructions related to such continued fractions (whenever possible). We say a few words about Minkowski–Voronoi continued fractions, triangle sequences related to Farey addition, O’Hara’s algorithm related to decomposition of rectangular parallelepipeds, geometric continued fractions, and determinant generalizations of continued fractions. Finally, we describe the relation of regular continued fractions to rational knots and links.

We do not pretend to give a complete list of generalizations of continued fractions. The idea is to show the diversity of generalizations.

Keywords

Continue Fraction Voronoi Tessellation Multidimensional Case Relative Minimum Euclidean Algorithm 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Oleg Karpenkov
    • 1
  1. 1.Dept. of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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