Changes

The length can be approximated by selecting a finite number of points along the curve and connecting the points with straight lines. The sum of the line segments can give a lower estimate for the length of the arc. The more points used, the closer the approximation to the curve. Technically, the arclength is the [[supremum]] of all such sums, represented as an [[integral]].For a curve that can be parametrised as <math>\vec{r}(t)</math>, the arclength from point <math>A</math> to <math>B</math> (with <math>t</math> being equal to <math>\alpha</math> and <math>\beta</math> at those points) can be found as <math>S = \int^{B}_{A} \, \text{d}s = \int^{\beta}_{\alpha} \vec{r}'(t) \cdot \vec{r}'(t) \, \text{d}t</math>