English

A geometrical approach to measure irrationality

Number Theory 2017-01-30 v2

Abstract

We present a geometric way of describing the irrationality of a number using the area of a circular sector A(r)A(r). We establish a connection between this and the continued fraction expansion of the number, and prove bounds for A(r)A(r) as rr\to\infty by describing the asymptotic behavior of the ratios of the denominators of the convergents.

Keywords

Cite

@article{arxiv.1511.09037,
  title  = {A geometrical approach to measure irrationality},
  author = {Pedro Morales-Almazan},
  journal= {arXiv preprint arXiv:1511.09037},
  year   = {2017}
}