Manuscripta Mathematica

, Volume 134, Issue 1–2, pp 157–169 | Cite as

Continued fractions and the second Kepler law

  • Oleg KarpenkovEmail author


In this paper we introduce a link between geometry of ordinary continued fractions and trajectories of points that moves according to the second Kepler law. We expand geometric interpretation of ordinary continued fractions to the case of continued fractions with arbitrary elements.

Mathematics Subject Classification (2000)

Primary 30B70 Secondary 53A04 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arnold V.I.: Continued Fractions. Moscow Center of Continuous Mathematical Education, Moscow (2002)Google Scholar
  2. 2.
    Arnold, V.I.: Ordinary Differential Equations, translated from the Russian by Roger Cooke. Second printing of the 1992 edition. Universitext, ii+334 pp. Springer, Berlin (2006)Google Scholar
  3. 3.
    Irwin M.C.: Geometry of continued fractions. Am. Math. Mon. 96(8), 696–703 (1989)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Karpenkov O.: On tori decompositions associated with two-dimensional continued fractions of cubic irrationalities. Funct. Anal. Appl. 38(2), 28–37 (2004)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Karpenkov O.: Elementary notions of lattice trigonometry. Math. Scand. 102(2), 161–205 (2008)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Karpenkov O.: On irrational lattice angles. Funct. Anal. Other Math. 2(2–4), 221–239 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Khinchin A.Y.: Continued Fractions. University of Chicago Press, Chicago (1964)zbMATHGoogle Scholar
  8. 8.
    Korkina E.I.: The simplest 2-dimensional continued fraction. J. Math. Sci. 82(5), 3680–3685 (1996)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Stark H.M.: An Introduction to Number Theory. Markham, Chicago (1970)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Technische Universität GrazGrazAustria

Personalised recommendations