Arc length

Arc length is the length of a curve from beginning to end. Conceptually, if we imagined the curve as a string, the arc length is how long the string would be if we straightened it out. It can be formalized mathematically for smooth curves using vector calculus and differential geometry, or for curves that might not necessarily be smooth as a smallest upper bound of lengths of polygonal chains. The curves for which this limit exists are called rectifiable curves, and the process of determining their arc length in this way is called curve rectification.