/sci/ - Science & Math

>>11159126
Correction: Not every curve's arc length can be computed this way. This assumes that the curve is a continuously differentiable function. Also, the arc length may vary based on what metric you use. As in >>11158784 there is another metric known as the taxicab metric where the distance between [math](x_1,\ldots,x_n) \in \mathbb{R}^n[/math] and [math](x_1',\ldots,x_n') \in \mathbb{R}^n[/math] is [math]\sum_{i=1}^n |x_i - x_i'|[/math] (basically summing up the absolute differences in each coordinate), and using that you can get 4 as the circumference of the unit circle.