Cayley's ruled cubic surface

{{Distinguish|Cayley's nodal cubic surface}}

In differential geometry, Cayley's ruled cubic surface is the ruled cubic surface

:$z=xy-x^3/3\; \backslash \; .$

In projective coordinates it is $zw^2\; =\; xyw\; -x^3/3\backslash$.

It contains a (double) line of self-intersection $x=w=0\backslash$and two pinch points.{{cite web |title=Ruled Cubics {{!}} Mathematical Institute |url=https://www.maths.ox.ac.uk/node/14691 |url-status=dead |archive-url=https://web.archive.org/web/20161110060139/https://www.maths.ox.ac.uk/node/14691 |archive-date=2016-11-10 |accessdate=2020-08-08 |website=www.maths.ox.ac.uk}}