Definition:Algebraic Curve/Degree

This page is about Degree of Algebraic Curve. For other uses, see Degree.

Definition

The degree of an algebraic curve is defined as the highest degree of the polynomial equations defining it.

Examples

Linear Curve

The Equation of Straight Line in Plane in Slope-Intercept Form:

$y = m x + c$

is an example of an algebraic curve which has degree $1$.

Example: $y^2 = 2 x$

The algebraic curve defined by the equation:

$y^2 = 2 x$

is an example of an algebraic curve which has degree $2$.

That is, it is a quadratic curve.

Example: $x y = 4$

The algebraic curve defined by the equation:

$y^2 = 2 x$

is an example of an algebraic curve which has degree $2$.

That is, it is a quadratic curve.

Also see

• Definition:Quadratic Curve
• Definition:Cubic Curve
• Definition:Quartic Curve
• Definition:Quintic Curve

• Results about degrees of algebraic curves can be found here.

Sources

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