English

When is the (co)sine of a rational angle equal to a rational number?

History and Overview 2010-06-16 v1

Abstract

If the cosine of a rational multiple of π\pi is a rational number then it is an integral multiple of 12\frac12. For this fact, we give a proof accessible to an interested school student. We then discuss which quadratic and cubic irrationalities are values of cosine at ratinal multiples of π\pi.

Keywords

Cite

@article{arxiv.1006.2938,
  title  = {When is the (co)sine of a rational angle equal to a rational number?},
  author = {Jörg Jahnel},
  journal= {arXiv preprint arXiv:1006.2938},
  year   = {2010}
}