Definition:Cubic Curve
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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)