arc length

When rectified, the curve gives a straight line segment with the same length as the curve's arc length. Arc length s of a logarithmic spiral as a function of its parameter θ

Arc length is the distance between two points along a curve. 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 limit 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.