In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

s that have the formula

Formula

In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....

:


Trident curves are cubic plane curves with an ordinary double point in the real projective plane

Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold, that is, a one-sided surface. It cannot be embedded in our usual three-dimensional space without intersecting itself...

 at x = 0, y = 1, z = 0; if we substitute x = x/z and y = 1/z into the equation of the trident curve, we get


which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves

Algebraic curve

In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...

 of genus

Geometric genus

In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds.-Definition:...

zero.