Differential geometry Curves in the plane and in space Concept
Total curvature
Summary
The total curvature of a curve is the integral of its curvature with respect to arc length. It measures how much the direction of the curve turns in all, from start to end. For closed curves it is bounded below by , by Fenchel's theorem, and knotted curves need more than , by the Fáry–Milnor theorem.
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| Tag | QP9DY5K8QW |
|---|---|
| URI | m2://QP9DY5K8QW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A04 |
| Same as | |
| Changed | 2 November 2026 |
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