Cassels, J. W. S. An introduction to Diophantine approximation. (English) Zbl 0077.04801 Cambridge Tracts in Mathematics and Mathematical Physics. No. 45. Cambridge: At the University Press, x, 166 p. (1957). Reviewer: Edmund Hlawka (Wien) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 445 Documents MSC: 11Jxx Diophantine approximation, transcendental number theory 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11Hxx Geometry of numbers 11Kxx Probabilistic theory: distribution modulo \(1\); metric theory of algorithms Keywords:Number Theory PDF BibTeX XML OpenURL Online Encyclopedia of Integer Sequences: Smallest integer q >= 1 such that difference between q*sqrt(2) and the nearest integer is <= 1/n. Decimal expansion of Lagrange(4) = sqrt(1517)/13. Numbers k(n) used for Cassels’s Markoff forms MF(n) corresponding to the conjectured unique Markoff triples MT(n) with maximal entry m(n) = A002559(n), for n >= 1. Numbers k(n) used for Markoff forms determining quadratic irrationals with purely periodic continued fractions. Discriminant a(n) of the indefinite binary quadratic Markoff form m(n)*F_{m(n)}(x, y) with m(n) = A002559(n), for n >= 1.