A Cubic Surface of Revolution
History and Overview
2013-07-23 v5
Abstract
We develop a direct and elementary (calculus-free) exposition of the famous cubic surface of revolution x^3+y^3+z^3-3xyz=1.12 pages. We have added a second elementary proof that the surface is of revolution.
Cite
@article{arxiv.1301.0243,
title = {A Cubic Surface of Revolution},
author = {Mark B. Villarino},
journal= {arXiv preprint arXiv:1301.0243},
year = {2013}
}
Comments
We12 pages. We have added a second elementary proof that the surface is of revolution. We have added a two proofs of a special case of the Salmon-Cayley theorem that every cubic surface has twenty-seven lines, a section on the singularities of cubic surfaces and material on the general problem of rational points on a cubic surface