Quartic plane curve
Appearance
A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:
This equation has fifteen constants. However, it can be multiplied by any non-zero constant without changing the curve. Therefore, the space of quartic curves can be identified with the real projective space . It also follows that there is exactly one quartic curve that passes through a set of fourteen distinct points in general position, since a quartic has 14 degrees of freedom.
A quartic curve can have a maximum of:
- Four connected components
- Twenty-eight bi-tangents
- Three ordinary double points.
Examples
- Bicorn curve
- Bullet-nose curve
- Cartesian oval
- Cassini oval
- Deltoid curve
- Hippopede
- Lemniscate of Bernoulli
- Lemniscate of Gerono
- Klein quartic
- Spiric section
- Toric section
- Kampyle of Eudoxus