# Questions tagged [arc-length]

For questions about/on finding the arc length of a curve/parametrized curve

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### How to use Crofton's Formula (Proving Arc of Great Circle Smallest Distance Between Points)

Problem. The shortest distance between points on the unit sphere is an arc of a great circle connecting them. Attempt: I followed the hints my professor gave and looked back at the proof of the ...
I’m trying to find the arc length of a curve and I only wanted to know if step 1 is correct so far then if I have trouble I’ll ask for help with my solution method Find the derivate $$r ( t ) = \... 0answers 27 views ### Three definitions of arc length Let \gamma:[0,1]\to M be a curve on a metric space (M,d). There are three ways to define the arc length of \gamma.$$\ell(\gamma):=\sup\bigg\{\sum_{i=0}^kd(\gamma(t_{i+1}),\gamma(t_i)):0=t_0&...
Let $y_0,y_1,x_1,\dots,x_N$ be distinct points in $\mathbb{R}^n$. Clearly there exists a piecewise linear curve $\gamma:[0,1]\rightarrow \mathbb{R}^n$ joining $y_0$ to $y_1$ for which  \min_{t \in [...