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Throughout history, angles have been measured in many different units. The most contemporary units are the degree and radian, but many others have been used throughout history. The purpose of this page is to aggregate other concepts pertaining to the angular unit, where additional explanation can be provided. ==Angle measurement in general== The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be ''equal'' or ''congruent'' or ''equal in measure''. In some contexts, such as identifying a point on a circle or describing the ''orientation'' of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the ''cumulative rotation'' of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent. In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the measure of the angle in radians. The measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor , where ''k'' is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians): : The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio ''s''/''r'' is unaltered. (Proof. The formula above can be rewritten as One turn, for which units, corresponds to an arc equal in length to the circle's circumference, which is 2''r'', so . Substituting ''n'' for ''θ'' and 2''r'' for ''s'' in the formula, results in = .}}) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Angular unit」の詳細全文を読む スポンサード リンク
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