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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.
A smooth arc is the graph of a continuous function whose. derivative is also continuous (so it does not have corner points). If the arc is just a straight line between two points of coordinates. (x1,y1), (x2,y2), its length can be found by the Pythagorean theorem: L =.