Degree (mathematics)
In mathematics, there are several meanings of degree depending on the subject.
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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 1⁄360 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 
is 
.
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
- ^ Beckmann P. (1976) A History of Pi, St. Martin's Griffin. ISBN 0-312-38185-9