[Etymology: Lat: ‘step’] Symbol ° generally, also deg. A step in any scale that is actually or figuratively discrete. When used in an ordinal manner, e.g. ‘second degree’, the degree often relates to gradations of authority, dignity, proficiency, or rank, with higher numeric values being superior. In other contexts, higher values can be seen as inferior. The common stance is that the terminology is open-ended at the numerically high end, leaving first degree tied to the anchor point from which to measure ascent or descent. For questioning, etc., the third degree is the implicit limit.
length 1/360 of a great circle of Earth, being 1 degree of longitude along the Equator
= 111.296~ km (69.156~ mi)else the similar but slightly variable 1° of latitude along a meridian
| near the Equator | = 110.551~ km (68.693~ mi) |
| near a Pole | = 111.669~ km (69.388~ mi) |
| at latitude ϕ | = (111.413 cos ϕ -0.094 cos 3ϕ) km. |
Also the very variable degree of longitude along an identified parallel of latitude, which ranges progressively down in size from the 111.296~ km at the Equator to zero at the Poles, closely proportional to cos ϕ.
See
minute for some derived units; see also
geographic mile.
plane angle. Symbol also arcdeg, degree of arc. The traditional measure, by definition = 1/360 of one revolution = 2π/360 rad = 0.017 453~ rad. Values are unlimited, but any value outside the range 0 to 360 represents identically the angle having the value within that range that differs by an integer multiple of 360. Thus the right angle, being 90°, is identically 450°, 810°, et seq., also -270°, -630°, et seq.
The figure 360 for degrees in the revolution appears to derive from the number of days in the year. The Chinese traditionally have 365¼ degrees in a revolution, one degree representing the average daily change in the rotating celestial scene, making this definition consistent with other aspirations to have ‘natural units’. Sumer, Babylon, else their precursors likely had the same initially, but then changed it to be a round number in their terms, specifically to an integer multiple of their number base, 60. The ready division of the circle into sixths, producing the regular hexagon of six equilateral triangles, would have encouraged this six-fold picture, each of the angles of these perfectly symmetric triangles being the base 60°. The 60° angle might be called a ‘hexangle’, in contrast to the right angle with its peculiar figure of 90°. Since the Babylonian-based scheme of 12 hours to the half-day persists for the clock (despite attempts to decimalize the clock along with length and mass), the use of 360° to girdle Earth is highly convenient, yielding 15° of longitude per hour of solar change. (Lest one think that 360 or 365¼ or the more accurate 365.242~ degrees per revolution is awkward, it should be noted that the SI standard, the radian, has 6.283 2~ units per revolution. This last is, of course, 2π, which places the radian close to the hexangle, which might be regarded as a primitive radian, using the crude but sometime used approximation π ≈ 3; see pi and Table 11.)
Table 11 | | | | | SI |
|---|
| second | … | … | … | … | 4.85~ μrad | |
| 60 | minute | … | … | … | 291.~ μrad | |
| 3600 | 60 | degree | … | … | 17.5~ mrad | |
| | 90 | right angle | … | 1.57~ rad | |
| | 180 | 2 | straight line | 3.14~ rad | =π rad |
| | 360 | 4 | 2 revolution | 6.28~ rad | = 2π rad |
See
square degree.
mathematics The power to which a variable is raised. For multi-term expressions, the maximal aggregate power of the variable(s) in a single term. Thus for the single-variable polynomial
x6 + 2x5 + 3x + 4
the degree is 6; for the multi-variable expression
x6 + 5x4y3z2 + 7x3y2 + 15y4z2
the degree is 4 + 3 + 2 = 9 (being greater than 6, 3 + 2, and 4 + 2).
statistics See degrees of freedom.
physics A unit in many scales for measuring temperature, e.g. Celsius (centigrade), Fahrenheit, Rankine (but not now the kelvin).
hydrometry 1912 As universal hydrometer degree, = 100 times the specific gravity. For petroleum products see API gravity.
viscometry The unit in the Engler and MacMichael systems for viscosity.
hardness of water The proportion of calcium salt, usually calcium carbonate (CaCO3):
English or Clark degree = grains of CaCO3 per gallon (1:70 000);
French degree = grams of CaCO3 per hectolitre (1:100 000);
German degree = grams of calcium oxide per hectolitre (1:100 000).The approximate relations are
5° English = 7° French = 4° German = 70 p.p.m. CaCO3,these figures being a commonly acknowledged ceiling for softness. Twice this concentration would make it definitely hard; three times is very hard.
photography The unit in the DIN and Scheiner systems for photographic emulsion speed, i.e. film speed.
geography As degrees of latitude and longitude, the angular offset of a point respectively from the plane of the Equator and the plane of the Greenwich meridian. See latitude.
medicine For burns, the respective degrees relate first to the epidermis, the second to the deeper skin tissues, the third to the underlying tissues.
See also Engler degree; proof.
