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Arc length - Wikipedia

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Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) 𝑓 : [ 𝑎 , 𝑏 ] → 𝑅 𝑛 , then the curve is rectifiable (i.e., it has a finite length). The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases. A curve in the plane can be approximated by connecting a finite number of points on the curve using (straight) line segments to create a polygonal path. Since it is straightforward to calculate the length of each linear segment (using the Pythagorean theorem in Euclidean space, for example), the total length of the approximation can be found by summation of the lengths of each linear segmen

Arc length - Wikipedia Jump to content From Wikipedia, the free encyclopedia Distance along a curve 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 cur

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