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Degree (Angle) - This article describes "degree" as a unit of angle. For alternative meanings, see Degree (disambiguation).
A degree (or in full degree of arc), usually symbolized by the symbol °, is a measurement of plane angles, or of a location along a great circle of a sphere (such as the Earth or the celestial sphere), representing 1/360 of a full rotation. The number 360 was probably adopted because it is readily divisible: it has 22 nontrivial factors, including every number from 2 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). 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 a different traditional subdivision is still 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". If still more accuracy is required, decimal divisions of the second are normally used, rather than thirds of 1/60 second. In mathematics, angles in degrees are rarely used, as the convenient divisibility of the number 360 is not so important. For various reasons mathematicians typically prefer to use the radian, an angle corresponding to an arc of a circle whose length equals the circle's radius. Thus 180 = π radians, 1 ≈ 0.0174533 radian, and 1 radian ≈ 57.29578. 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, and there would be 400 decimal degrees in a circle. This idea did not gain momentum.
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