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A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [4] It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. [5]
The angle expressed by another angular unit may then be obtained by multiplying the angle by a suitable conversion constant of the form k / 2 π , where k is the measure of a complete turn expressed in the chosen unit (for example, k = 360° for degrees or 400 grad for gradians):
360 is a triangular matchstick number. [4] 360 is the product of the first two unitary perfect numbers: [5] = There are 360 even permutations of 6 elements. They form the alternating group A 6. A turn is divided into 360 degrees for angular measurement. 360° = 2 π rad is also called a round angle.
[18] [19] Today, the degree, 1 / 360 of a turn, or the mathematically more convenient radian, 1 / 2 π of a turn (used in the SI system of units) is generally used instead. In the 1970s – 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions . [ 23 ]
Degree (angle), a unit of angle measurement Degree of geographical latitude; Degree of geographical longitude; Degree symbol (°), a notation used in science, engineering, and mathematics; Degree (temperature), any of various units of temperature measurement; Degree API, a measure of density in the petroleum industry; Degree Baumé, a pair of ...
For example, the arithmetic mean of 0° and 360° is 180°, which is misleading because 360° equals 0° modulo a full cycle. [1] As another example, the "average time" between 11 PM and 1 AM is either midnight or noon, depending on whether the two times are part of a single night or part of a single calendar day.
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An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which is expressed here using the Greek letter tau (τ). Some special angles in radians, stated in terms of 𝜏. A comparison of angles expressed in degrees and radians.