Question

What is the arclength between two points on a curve? How does it differ from the distance?

Answer 1

The distance is the arc length on a straight line. The arc length is the distance along the arc.

Explanation:

Example

For the points `(-1,0)` and `(1,0)`,

the distance between the points (the length of the straight line joining them) is `2`.

The length of the arc on the unit circle: `x^2+y^2=1` is half the circumference, so it is `pi`. (More completely, the lengths of both the upper and lower arcs are `pi`.)