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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 circle is such a common shape that we take it for granted ... but there is more to it that just a common shape. Mathematically, the circle is defined as the set of all points that are the same distance from a given point, called the center. That distance is called the radius. The word radius comes from the Latin word for rod or spoke of a wheel, and the radii, or spokes, radiate out from the center.