differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, Cayley's ruled cubic surface is the ruled

cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than ...

z=xy-x^3/3 \ .

In projective coordinates it is

zw^2 = xyw -x^3/3\

. It contains a (double) line of self-intersection

x=w=0\

and two pinch points.

References

External links

Cubical ruled surface
* {{DEFAULTSORT:Cayley's Ruled Cubic Surface Algebraic surfaces Differential geometry