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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 arc length will be continuously calculated. The arc length is the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints (which would be a chord) There is a shorthand way of writing the length of an arc: This is read as The length of the arc AB is 10. The lower case L in the front is short for 'length'. However, in many cases the letter L and even the curved line over the AB is left out if there is no doubt about what is meant. Central angle in degrees. The formula the arc measure is: where: Recall that 2ÏR is the circumference of the whole circle, so the formula simply reduces this by the ratio of the arc angle to a full angle (360). By transposing the above formula, you solve for the radius, central angle, or arc length if you know any two of them. Central angle in radians*