Definition:Algebraic Curve/Degree
< Definition:Algebraic Curve(Redirected from Definition:Degree of Algebraic Curve)
Jump to navigation
Jump to search
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): degree: 2. (of a curve)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): order: 3. (of a curve or surface)
- 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)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): order: 3. (of a curve or surface)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebraic curve
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebraic curve