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Encyclopedia > Degree (angle)
This article describes the unit of angle. For other meanings, see degree.

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 1360 of a full rotation. 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] Image File history File links Emblem-important. ... Look up degree in Wiktionary, the free dictionary. ... This article describes the typographical or mathematical symbol. ... This article is about the mathematical construct. ... This article is about angles in geometry. ... On the earth, a meridian is a north-south line between the North Pole and the South Pole. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the... A sphere is a symmetrical geometrical object. ... Map of Earth showing lines of latitude (horizontally) and longitude (vertically), Eckert VI projection; large version (pdf, 1. ... Adjectives: Martian Atmosphere Surface pressure: 0. ... The celestial sphere is divided by the celestial equator. ...

Contents

History

The number 360 as the number of 'degrees' (i.e. smallest practical sub-arcs) in a circle, and hence the unit of a degree as a sub-arc of 1360 of the circle, was probably adopted because it approximates the number of days in a year. Its use is often said to originate from the methods of the ancient Babylonians.[2] Ancient astronomers noticed that the stars in the sky, which circle the celestial pole every day, seem to advance in that circle by approximately one-360th of a circle, i.e. one degree, each day. Primitive calendars, such as the Persian Calendar used 360 days for a year. Its application to measuring angles in geometry can possibly be traced to Thales who popularized geometry among the Greeks and lived in Anatolia (modern western Turkey) among people who had dealings with Egypt and Babylon. 360(Three hundred sixty) is the natural number following 359 and preceding 361. ... Babylonia was an ancient state in Iraq), combining the territories of Sumer and Akkad. ... An astronomer or astrophysicist is a scientist whose area of research is astronomy or astrophysics. ... The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... A page from the Hindu calendar 1871-72. ... This article is in need of attention. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... Thales of Miletos (, ca. ...


Another motivation for choosing the number 360 is that it is readily divisible: 360 has 24 divisors (including 1 and 360), including every number from 1 to 10 except 7. For the number of degrees in a circle to be divisible by every number from 1 to 10, there would need to be 2520 degrees in a circle, which is a much less convenient number. In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ...

Divisors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

India

The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rig Veda: The Rig Veda ऋग्वेद (Sanskrit ṛc praise + veda knowledge) is the earliest of the four Hindu religious scriptures known as the Vedas. ...

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.
(Dirghatama, Rig Veda 1.164.48)

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, but the traditional sexagesimal unit subdivision is commonly seen. 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, or if necessary by a single and double closing quotation mark: for example, 40.1875° = 40° 11' 15". For other uses, see Astronomy (disambiguation). ... This article is about the geographical term. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... For other uses, see Decimal (disambiguation). ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... The former Weights and Measures office in Middlesex, England. ... A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 ≈ 7. ... This article is not about the symbol for the set of prime numbers, â„™. The prime (′, Unicode U+2032, ′) is a symbol with many mathematical uses: A complement in set theory: A′ is the complement of the set A A point related to another (e. ...


If still more accuracy is required, decimal divisions of the second are normally used, rather than thirds of 160 second, fourths of 160 of a third, and so on. These (rarely used) subdivisions were noted 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. The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ...


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 circle (360°) is equal to 2π radians, so 180° is equal to π radians, or equivalently, the degree is a mathematical constant ° = π180. This article is about angles in geometry. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Some common angles, measured in radians. ... In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. ...


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 did not gain much momentum, most scientific calculators support it. The International System of Units (symbol: SI) (for the French phrase Syst me International dUnit s) is the most widely used system of units. ... The grad is a measurement of plane angles of value 1/400 of a full circle, thus dividing a right angle in 100. ... For other uses, see Calculator (disambiguation). ...


An angular mil which is most used in military applications has at least three specific variants. The mil (in full, angular mil) is a unit of angular measure. ...


In computer games which depict a three-dimensional virtual world, the need for very fast computations resulted in the adoption of a binary, 256 degree system. In this system, a right angle is 64 degrees, angles can be represented in a single byte, and all trigonometric functions are implemented as small lookup tables. These units are sometimes called "binary radians" ("brads") or "binary degrees".[citation needed]


See also

Some common angles, measured in radians. ... The gon is a measurement of plane angles, corresponding to 1/400 of a full circle, thus dividing a right angle in 100. ... A square degree is a non-SI unit that can be used to measure solid angles (that is, the area of the projection of a surface onto a unit sphere centered on the point of observation). ... The steradian (ste from Greek stereos, solid) is the SI derived unit of solid angle, and the 3-dimensional equivalent of the radian. ... This article is about the navigational instrument. ... Map of Earth showing lines of latitude (horizontally) and longitude (vertically), Eckert VI projection; large version (pdf, 1. ...

References

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

External links


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