# Degree (mathematics)

Degree (mathematics)

In mathematics, there are several meanings of degree depending on the subject.

## Unit of angle

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, representing 1360 of a turn. When that angle is with respect to a reference meridian, it indicates a location along a great circle of a sphere, such as Earth (see Geographic coordinate system), Mars, or the celestial sphere.[1]

## Degree of a monomial

The degree of a monomial is equal to sum of the exponents of each of the variables appearing in the monomial, e.g. the degree of x2yz3 is 2 + 1 + 3.

## Degree of a field extension

Given a field extension K/F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by [K : F].

## Degree of a vertex in a graph

In graph theory, the degree of a vertex in a graph is the number of edges incident to that vertex — in other words, the number of lines coming out of the point. In a directed graph, the indegree and outdegree count the number of directed edges coming into and out of a vertex respectively.

## Topological degree

In topology the term degree is used for various generalizations of the winding number in complex analysis. See topological degree theory.

## Degree of freedom

A degree of freedom is a concept in mathematics, statistics, physics and engineering. See degrees of freedom.

## References

1. ^ Beckmann P. (1976) A History of Pi, St. Martin's Griffin. ISBN 0-312-38185-9

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