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.


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

Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Degree — may refer to: Contents 1 As a unit of measurement 2 In mathematics 3 In education …   Wikipedia

  • Degree of a polynomial — The degree of a polynomial represents the highest degree of a polynominal s terms (with non zero coefficient), should the polynomial be expressed in canonical form (i.e. as a sum or difference of terms). The degree of an individual term is the… …   Wikipedia

  • Degree of a continuous mapping — This article is about the term degree as used in algebraic topology. For other uses, see degree (mathematics). A degree two map of a sphere onto itself. In topology, the degree is a numerical invariant that describes a continuous mapping between… …   Wikipedia

  • Mathematics and art — have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid,[1] the Parthenon …   Wikipedia

  • Degree programs at Boston College — are offered in over 50 fields in 11 schools and colleges. [cite web | url = | title = About Boston College | accessdate = 2006 08 15] Departments and majorsCollege of Arts Sciences /School of Arts Sciences *African and… …   Wikipedia

  • degree — In Sheridan s The Rivals (1775), we find the assertion Assuredly, sir, your father is wrath to a degree, meaning ‘your father is extremely cross’. The use survived in more florid English into the 20c and was accepted by Fowler (1926) ‘however… …   Modern English usage

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics       Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity.       Computer scientist Manindra Agrawal of the… …   Universalium

  • mathematics, East Asian — Introduction       the discipline of mathematics as it developed in China and Japan.       When speaking of mathematics in East Asia, it is necessary to take into account China, Japan, Korea, and Vietnam as a whole. At a very early time in their… …   Universalium

  • Mathematics Genealogy Project — The Mathematics Genealogy Project is a web based database for the academic genealogy of mathematicians.[1][2][3] As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to research level… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”