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

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

s that have the formula: :

xy+ax^3+bx^2+cx=d

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

real projective plane In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has b ...

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

ax^3+bx^2z+cxz^2+xz = dz^3,

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

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...

zero.

References

External links

* Algebraic curves {{algebraic-geometry-stub