Definition:Algebraic Curve/Degree

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This page is about the degree of an 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 known as

The degree of an algebraic curve is also known as its order.


Also see

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


Sources