A curve in the plane can be approximated by connecting a finite number of points on the curve using (straight)
If … See more

Let be an injective and continuously differentiable (i.e., the derivative is a continuous function) function. The length of the curve defined by can be defined as the limit of the sum of linear segment lengths for a regular p… See more

If a planar curve in is defined by the equation where is continuously differentiable, then it is simply a special case of a parametric equation where and The Euclidean distance of each infinitesimal segment of the arc can be given by: … See more

Arc lengths are denoted by s, since the Latin word for length (or size) is spatium.
In the following lines, represents the radius of a circle, is its diameter, is its circumference, is the length of an arc of the circle, and is the angle whic… See more

For much of the history of mathematics, even the greatest thinkers considered it impossible to compute the length of an irregular arc. Although Archimedes had pioneered a way of finding the area beneath a … See more

As mentioned above, some curves are non-rectifiable. That is, there is no upper bound on the lengths of polygonal approximations; the length can be made arbitrarily large. Informally, such curves are said to have infinite leng… See more

• Arc (geometry)
• Circumference
• Crofton formula
• Elliptic integral
• Geodesics… See more