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GeezerVison is showing mathworld.wolfram.com — Curve Length -- from Wolfram MathWorld

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Curve Length

The curve length of a smooth curve gamma:[0,1]->M in a Riemannian manifold M is

int_0^1|gamma^'(t)|_(gamma(t))dt.

Here gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x, and |gamma^'(t)|_(gamma(t)) is the norm determined by the Riemannian structure.

See also

Arc Length, Distance, Length Metric

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Cite this as:

Weisstein, Eric W. "Curve Length." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CurveLength.html

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