English

Ford circles, continued fractions, and best approximation of the second kind

Number Theory 2009-12-11 v1 Metric Geometry

Abstract

We give an elementary geometric proof using Ford circles that the convergents of the continued fraction expansion of a real number α\alpha coincide with the rationals that are best approximations of the second kind of α\alpha.

Keywords

Cite

@article{arxiv.0912.1997,
  title  = {Ford circles, continued fractions, and best approximation of the second kind},
  author = {Ian Short},
  journal= {arXiv preprint arXiv:0912.1997},
  year   = {2009}
}

Comments

8 pages, 6 figures