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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.
Arc: a curved line that is part of the circumference of a circle. The arc of the circle is measured in degrees or radians - for example: 90Â° or $\frac{\pi}{2}$ - a quarter of the circle, 180Â° or $\pi$ - a half of the circle. The arc is smaller than 360Â°(or $2\pi$) because that is the whole circle.