Degree

Degree may refer to:

As a unit of measurement

Field extension

In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x² = 2.

Definitions

Let L be a field. A subfield of L is a subset K of L that is closed under the field operations of L and under taking inverses in L. In other words, K is a field with respect to the field operations inherited from L. The larger field L is then said to be an extension field of K. To simplify notation and terminology, one says that L / K (read as "L over K") is a field extension to signify that L is an extension field of K.

If L is an extension of F which is in turn an extension of K, then F is said to be an intermediate field (or intermediate extension or subextension) of the field extension L / K.

Degree symbol

The degree symbol (°) is a typographical symbol that is used, among other things, to represent degrees of arc (e.g. in geographic coordinate systems), hours (in the medical field), degrees of temperature, alcohol proof, or diminished quality in musical harmony. The symbol consists of a small raised circle, historically a zero glyph.

In Unicode it is encoded at U+00B0 ° DEGREE SIGN (HTML ° · °).

History

The first known recorded modern use of the degree symbol in mathematics is from 1569 where the usage seems to show that the symbol is a small raised zero, to match the prime symbol notation of sexagesimal subdivisions of degree such as minute ′, second ″, and tertia ‴ which originates as small raised Roman numerals.

Typography

In the case of degrees of arc, the degree symbol follows the number without any intervening space.