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CHASLES CUBIC


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.
 
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© Robert FERRÉOL 2017