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There are a number of meanings for the word arc in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. In a graph, a graph arc is an ordered pair of adjacent vertices. In particular, an arc is any portion (other than the entire curve) of the circumference of a circle. An arc corresponding to the central angle is denoted . Similarly, the size of the central angle subtended by this arc (i.e., the measure of the arc) is sometimes (e.g., Rhoad et al.
The circumference subtends an angle of 2Ï radians. The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at A072097).