Karpenkov, Oleg Continued fractions and the second Kepler law. (English) Zbl 1422.11155 Manuscr. Math. 134, No. 1-2, 157-169 (2011). Summary: 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. Cited in 2 Documents MSC: 11J70 Continued fractions and generalizations 30B70 Continued fractions; complex-analytic aspects 70F05 Two-body problems PDF BibTeX XML Cite \textit{O. Karpenkov}, Manuscr. Math. 134, No. 1--2, 157--169 (2011; Zbl 1422.11155) Full Text: DOI arXiv References: [1] Arnold V.I.: Continued Fractions. Moscow Center of Continuous Mathematical Education, Moscow (2002) [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) [3] Irwin M.C.: Geometry of continued fractions. Am. Math. Mon. 96(8), 696–703 (1989) · Zbl 0702.11038 · doi:10.2307/2324717 [4] Karpenkov O.: On tori decompositions associated with two-dimensional continued fractions of cubic irrationalities. Funct. Anal. Appl. 38(2), 28–37 (2004) · Zbl 1125.11042 · doi:10.1023/B:FAIA.0000034040.08573.22 [5] Karpenkov O.: Elementary notions of lattice trigonometry. Math. Scand. 102(2), 161–205 (2008) · Zbl 1155.11035 [6] Karpenkov O.: On irrational lattice angles. Funct. Anal. Other Math. 2(2–4), 221–239 (2009) · Zbl 1246.11128 · doi:10.1007/s11853-008-0029-9 [7] Khinchin A.Y.: Continued Fractions. University of Chicago Press, Chicago (1964) · Zbl 0117.28601 [8] Korkina E.I.: The simplest 2-dimensional continued fraction. J. Math. Sci. 82(5), 3680–3685 (1996) · Zbl 0901.11003 · doi:10.1007/BF02362573 [9] Stark H.M.: An Introduction to Number Theory. Markham, Chicago (1970) · Zbl 0198.06401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.