Definition:Algebraic Curve/Degree

This page is about degree of algebraic curve. For other uses, see degree.

Definition

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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)