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 is a rational number then it is an integral multiple of . 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 .
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}
}