degree
American Heritage Dictionary:
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de·gree
(dĭ-grē') 
n.
n.
- One of a series of steps in a process, course, or progression; a stage: proceeded to the next degree of difficulty.
- A step in a direct hereditary line of descent or ascent: First cousins are two degrees from their common ancestor.
- Relative social or official rank, dignity, or position.
- Relative intensity or amount, as of a quality or attribute: a high degree of accuracy.
- The extent or measure of a state of being, an action, or a relation: modernized their facilities to a large degree.
- A unit division of a temperature scale.
- Mathematics. A planar unit of angular measure equal in magnitude to 1/360 of a complete revolution.
- A unit of latitude or longitude, equal to 1/360 of a great circle.
- Mathematics.
- The greatest sum of the exponents of the variables in a term of a polynomial or polynomial equation.
- The exponent of the derivative of highest order in a differential equation in standard form.
- An academic title given by a college or university to a student who has completed a course of study: received the Bachelor of Arts degree at commencement.
- A similar title conferred as an honorary distinction.
- Law. A division or classification of a specific crime according to its seriousness: murder in the second degree.
- A classification of the severity of an injury, especially a burn: a third-degree burn.
- Grammar. One of the forms used in the comparison of adjectives and adverbs. For example, tall is the positive degree, taller the comparative degree, and tallest the superlative degree of the adjective tall.
- Music.
- One of the seven notes of a diatonic scale.
- A space or line of the staff.
by degrees
- Little by little; gradually.
- To a small extent; in a limited way: doesn't like spicy food, but can eat a little pepper to a degree.
[Middle English degre, from Old French, from Vulgar Latin *dēgradus : Latin dē-, de- + Latin gradus, step.]
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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 20th century and was accepted by Fowler (1926) 'however illogical it seems'. But this meaning is now dated, and in current use to a degree means 'to some extent' rather than 'to a great extent' and this is what will be understood if the word degree is not qualified:
W. J. Bryan was to a degree exceptional even in the USA—P. Wiles, 1969.To avoid any doubt, qualify the word degree in some way, as in to a large degree / to a certain degree / to some degree / to an amazing degree etc. The informal phrase to the nth degree (taken from mathematics) means 'to a very great degree' or 'indefinitely'.
| defuse, diffuse, deflection, definite, definitive | |
| deify, deity, deliberative, deliver |
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[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.)
| 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 |
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 + 4the degree is 6; for the multi-variable expression
x6 + 5x4y3z2 + 7x3y2 + 15y4z2the 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.
Roget's Thesaurus:
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degree
noun
- One of the units in a course, as on an ascending or descending scale: grade, level, peg, point, rung, stage, step. Informal notch. See big/small/amount.
- Relative intensity or amount, as of a quality or attribute: extent, magnitude, measure, proportion. See big/small/amount.
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The position of a note in a diatonic scale. The first degree is the tonic, the second the supertonic, the third the mediant, the fourth the subdominant, the fifth the dominant, the sixth the submediant, and the seventh the leading note.
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The degree of a predicate is the number of terms with which it must be combined to give a well-formed sentence. If the number is one, the predicate is monadic (e.g. ‘… is a man’), if two then it is dyadic or binary (… is brother of …), and so on. In classical formal language the degree or ‘adicity’ of a predicate is fixed, but there is no theoretical bar to predicates of variable adicity (‘… cooked supper together’).
1. A unit of angular distance. One degree equals 1/360 revolutions of a circle.
2. The loft of a golf-club that is usually given as the number of degrees the club-face is set back from the vertical
3. Unit of temperature.
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This entry contains information applicable to United States law only.
Extent, measure, or scope of an action, condition, or relation. Legal extent of guilt or negligence. Title conferred on graduates of school, college, or university. The state or civil condition of a person. The grade or distance one thing may be removed from another; i.e., the distance, or number of removes that separate two persons who are related by consanguinity. Thus, a sibling is in the second degree of kinship but a parent is in the first degree of kinship.
Unit Conversions:
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degrees (angle)
To convert from degrees (angle) to:
quadrants,
multiply by .01111.
radians,
multiply by .01745.
seconds,
multiply by 3600.
Related measurements:
degrees/sec
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Word Tutor:
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degree
IN BRIEF: A stage in the progress of something. Also: a unit used in measuring temperature.
She advanced by degrees from office clerk to president.
Tutor's tip: The mayor's "decree' (a legal or religious order) reduced the "degree" (the extent or amount of something) of graffiti downtown.
LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!
Sign Language Videos:
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degree
as in: academic credential
sign description: Both F-hand begin together and are pulled apart.
sign description: Both F-hand begin together and are pulled apart.
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In geometry, a unit of measurement of angles, 1/360 of a circle. In physics, a unit of temperature (see Celsius, Fahrenheit, and Kelvin scale). A degree on the Fahrenheit scale is smaller than a degree on the Celsius or Kelvin scale. Degrees on the Celsius and Kelvin scales are the same size.
Wiley Dictionary of Flavors:
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Degree
- A measuring device, usually regarding temperature. Common temperature measuring ranges are degrees Kelvin (using Absolute 0 as 0 = -273°C); degrees Celsius (Centigrade) (using 0° as the freezing point of water and 100° as the boiling point of water; and degrees Fahrenheit (using 32° as the freezing point of water and 212° as the boiling point of water. See Temperature.
- A title bestowed upon a student upon completion of a minimum set of requirements in a certain subject concentration. Although there are no degrees in Flavor Chemistry that are available to the author's knowledge, most flavor chemists have a background in the sciences. However, this is not a requirement for entry into the Society of Flavor Chemists.
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1. a grade or rank awarded scholars by a college or university.
2. a unit of measure of temperature.
3. a unit of measure of arcs and angles, one degree being 1/360 of a circle.
Random House Word Menu:
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categories related to 'degree'
- Maps and Cartography - degree: unit of measurement for latitude and longitude
- Quantities, Relationships, and Operations - degree: unit of angular measure; measure around fixed point, with total of 360 degrees in circle
- U.S. System - degree: unit of angular or circular measure equal to 60 minutes or 1360 of a circle
- Colleges and Universities - degree: title conferred by college for completion of course of study or in honorary recognition
- Harmony, Melody, and Structure - degree: tone or step of the scale
See crossword solutions for the clue Wikipedia on Answers.com:
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Degree (angle)
ninety degrees (shown in blue)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians. It is not an SI unit, as the SI unit for angles is radian, but it is mentioned in the SI brochure as an accepted unit.[1]
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Contents
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History
The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.[2] Ancient astronomers noticed that the sun, that follows through the ecliptic path over the course of the year, seems to advance in that path by approximately one degree, each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The Mayans used 20 cycles of 18 plus 5 unlucky days in one of their Maya calendars. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.
Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.[3] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.
Aristarchus of Samos and Hipparchos seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.[4] Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes (DIO 14 ‡2 p.19 n.24). Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.
The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda:[5]
Twelve spokes, one wheel, navels three.
Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.— Dirghatamas , Rigveda 1.164.48
Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors, making it one of only 7 numbers that have more divisors than any number twice itself (sequence A072938 in OEIS)[6][7]. Furthermore, it is divisable by every number from 1 to 10 except 7.[8] This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.
Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.
Subdivisions
For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for latitudes and longitudes on the Earth, degree measurements may be written with decimal places like 40.1875° with the degree symbol behind the decimals.
Alternatively, the traditional sexagesimal unit subdivision can be used. One degree is divided into 60 minutes (of arc), and one minute into 60 seconds (of arc). These units, also called the arcminute and arcsecond, are respectively represented as a single and double prime: for example, 40.1875° = 40° 11′ 15″ . Sometimes single and double quotation marks are used instead: 40° 11' 15" .
If still more accuracy is required, current practice is to use decimal divisions of the second like 40° 11′ 15.4″ . The older system of thirds, fourths, etc., which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today. These subdivisions were denoted[citation needed] by writing the Roman numeral for the number of sixtieths in superscript: 1I for a "prime" (minute of arc), 1II for a second, 1III for a third, 1IV for a fourth, etc. Hence the modern symbols for the minute and second of arc, and the word "second" also refer to this system.[citation needed]
Alternative units
See also: Measuring angles
In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2π radians, so 180° is equal to π radians, or equivalently, the degree is a mathematical constant: 1° = π⁄180.
The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. 1 turn = 360°.
With the invention of the metric system, based on powers of ten, there was an attempt to define a "decimal degree" (grad or gon), so that the number of decimal degrees in a right angle would be 100 gon, and there would be 400 gon in a circle. Although this idea was abandoned already by Napoleon, some groups have continued to use it and many scientific calculators still support it.
An angular mil, which is most used in military applications, has at least three specific variants, ranging from 1⁄6400 to 1⁄6000, each approximately equal to one milliradian. However, 1⁄6000 used by the Russian Army originated in Imperial Russia, where an equilateral chord was divided into tenths to give a circle of 600 units (this may be seen on a protractor, circa 1900, in the St Petersberg Museum of Artillery).
Conversion of some common angles
| Units | Values | |||||||
|---|---|---|---|---|---|---|---|---|
| Turns | 0 | 1⁄12 | 1⁄8 | 1⁄6 | 1⁄4 | 1⁄2 | 3⁄4 | 1 |
| Degrees | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| Radians | 0 |  |
 |
 |
 |
 |
 |
 |
| Grads | 0g | 33⅓g | 50g | 66⅔g | 100g | 200g | 300g | 400g |
See also
Notes
- ^ http://www.bipm.org/en/si/si_brochure/chapter4/table6.html
- ^ Degree, MathWorld
- ^ J.H. Jeans (1947), The Growth of Physical Science, p.7; Francis Dominic Murnaghan (1946), Analytic Geometry, p.2
- ^ For more information see D.Rawlins on Aristarchus; and G. J. Toomer, "Hipparchus and Babylonian astronomy."
- ^ Dirghatamas, Rigveda 1.164.48
- ^ Divisibility highly composite numbers, Werner Brefeld
- ^ The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
- ^ Contrast this with the relatively unwieldy 2520, which is the least common multiple for every number from 1 to 10.
External links
 |
Wikimedia Commons has media related to: Degree (angle) |
- Degrees as an angle measure, with interactive animation
- Degree at MathWorld
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This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
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Degree
idioms:
- by degrees gradvist
- degrees Celsius grader celsius
- degrees centigrade grader på hundredegradsskala, grader celsius
- degrees Fahrenheit grader fahrenheit
- to the nth degree i n'te potens, i højeste potens, til det yderste
Nederlands (Dutch)
mate, hoogte (waarin), graad (temperatuur/hoek etc.), academische graad
Français (French)
n. - (Géog, Math) degré, degré (température), rang, échelon, (un) certain, nombreux, (Univ) diplôme, licence, (Ling) degré, rang (social)
idioms:
- by degrees par degrés
- degrees Celsius degrés Celsius
- degrees centigrade degrés centigrades
- degrees Fahrenheit degrés Fahrenheit
- to the nth degree jusqu'au -nième degré
Deutsch (German)
n. - Grad, Stufe, Hochschulabschluß
idioms:
- by degrees nach und nach
- degrees Celsius Grad Celsius
- degrees centigrade Grad Celsius
- degrees Fahrenheit Grad Fahrenheit
- to the nth degree übertrieben
Ελληνική (Greek)
n. - βαθμός, βαθμίδα, στάδιο, διαβάθμιση, ακαδημαϊκός τίτλος, πανεπιστημιακό πτυχίο, (μαθημ.) μοίρα κύκλου, (για κατάσταση ή σχέση) βαθμός, έκταση, (γραμμ.) βαθμός (παραθετικών), (νομ.) βαθμός ενοχής ή υπαιτιότητας
idioms:
- by degrees βαθμιαία, βαθμηδόν
- degrees Celsius βαθμοί Κελσίου
- degrees centigrade βαθμοί Κελσίου
- degrees Fahrenheit βαθμοί Φαρενάιτ
- to the nth degree στη νιοστή δύναμη
Italiano (Italian)
grado, laurea
idioms:
- by degrees gradualmente
- degrees Celsius gradi centigradi
- degrees centigrade gradi centigradi
- degrees Fahrenheit gradi Fahrenheit
- to the nth degree all'ennesima potenza
Português (Portuguese)
n. - grau (m)
idioms:
- by degrees passo a passo
- degrees Celsius graus (m pl) Celsius
- degrees centigrade graus (m pl) centígrados
- degrees Fahrenheit graus (m pl) Fahrenheit
- to the nth degree no mais alto grau
Русский (Russian)
степень, градус, положение
idioms:
- by degrees постепенно
- degrees Celsius шкала Цельсия
- degrees centigrade шкала Цельсия
- degrees Fahrenheit шкала Фаренгейта
- to the nth degree в определенной степени, до крайней степени
Español (Spanish)
n. - grado, título, licenciatura, categoría, diferentes pasos, cantidad, rango, clasificación, etapa, punto
idioms:
- by degrees poco a poco, gradualmente
- degrees Celsius grados Celsius
- degrees centigrade grados centígrados
- degrees Fahrenheit grados Fahrenheit
- to the nth degree en sumo grado, al máximo
Svenska (Swedish)
n. - grad, rang, värdighet, ställning
中文（简体）(Chinese (Simplified))
程度, 学位, 度数
idioms:
- by degrees 渐渐, 逐渐
- degrees Celsius 摄氏温度
- degrees centigrade 百分度, 摄氏度
- degrees Fahrenheit 华氏温度
- to the nth degree 极度地, 极端地
中文（繁體）(Chinese (Traditional))
n. - 程度, 學位, 度數
idioms:
- by degrees 漸漸, 逐漸
- degrees Celsius 攝氏溫度
- degrees centigrade 百分度, 攝氏度
- degrees Fahrenheit 華氏溫度
- to the nth degree 極度地, 極端地
한국어 (Korean)
n. - 각도, 범죄의 등급, 정도
idioms:
- by degrees 점점
- to the nth degree 극도로
日本語 (Japanese)
n. - 程度, 段階, 親等, 級, 学位, 資格, 階級, 次
idioms:
- by degrees 次第に
- honours degree 優等学位
العربيه (Arabic)
(الاسم) وحدة لقياس, الزوايا, وحدة لقياس, الحرارة ( درجه) , درجه, مدى, مؤهل أو شهادة جامعيه
עברית (Hebrew)
n. - תואר, מעלה, דרגה, מידה
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