red: elliptic cubic with an oval  green: acnodal cubic  blue: elliptic cubic with an infinite branch  yellow: crunodal cubic  magenta: cuspidal cubic

 

Michel Chasles (1793, 1880): French mathematician.

 

Cartesian equation:  , where a ¹ 0 (in other words, y is a homogeneous polynomial of degree 3 in x and y). Cubic.

The homographic tranformation:  reduces this Chasles cubic to the divergent parabola.

Like the divergent parabolas (as well as the cubic hyperbolas), the Chasles cubics represent the perspectives of all cubics.
 

next curve

previous curve

2D curves

3D curves

surfaces

fractals

polyhedra

© Robert FERRÉOL 2017