Geometry of Regular Continued Fractions

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


Continued fractions play an important role in the geometry of numbers. In this chapter we describe a classical geometric interpretation of regular continued fractions in terms of integer lengths of edges and indices of angles for the boundaries of convex hulls of all integer points inside certain angles. In the next chapter we will extend this construction to construct a complete invariant of integer angles. For the geometry of continued fractions with arbitrary elements see Chap.  11.


Convex Hull Extremal Point Break Line Rational Number Arbitrary Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

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

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