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 … 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, $${\displaystyle r}$$ represents the radius of a circle, $${\displaystyle d}$$ is its diameter, $${\displaystyle C}$$ 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 continuous … 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, … See more

Antiquity
For much of the history of mathematics, even the greatest thinkers considered it impossible to … See more

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