Definition:Cubic Curve

Definition

A quadratic curve is an algebraic curve which has degree $3$.

That is, a cubic curve is an algebraic curve which is the locus of an equation of the $3$rd degree.

Examples

Folium of Descartes

The folium of Descartes is an example of a cubic curve:

Cartesian Form

The folium of Descartes is the locus of the equation:

$x^3 + y^3 - 3 a x y = 0$

Also see

• Results about cubic curves can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cubic
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): degree: 2. (of a curve)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cubic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): degree: 2. (of a curve)