English

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.

Keywords

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

R2 v1 2026-06-21T23:02:56.282Z