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 See more

If a planar curve in $${\displaystyle \mathbb {R} ^{2}}$$ is defined by the equation $${\displaystyle y=f(x),}$$ where $${\displaystyle f}$$ is continuously differentiable, then it is simply a special case of a parametric equation where $${\displaystyle x=t}$$ See more

As mentioned above, some curves are non-rectifiable. That is, there is no upper bound on the lengths of polygonal approximations; the … See more

Let $${\displaystyle f\colon [a,b]\to \mathbb {R} ^{n}}$$ be an injective and continuously differentiable (i.e., the derivative is a … See more

Arcs of circles
Arc lengths are denoted by s, since the Latin word for length (or size) is spatium.
In the following lines, See more

Antiquity
For much of the history of mathematics, even the greatest thinkers considered it impossible to compute the length of an irregular arc. Although See more

• Arc (geometry)
• Circumference
• Crofton formula
• See more