Differential geometry Curves in the plane and in space Concept
Curvature of a curve
Summary
The curvature of a curve measures how fast its direction turns per unit of length travelled. For a unit-speed curve it is the length of the acceleration vector. A straight line has curvature and a circle of radius has curvature . Curvature, together with torsion, determines a space curve up to a rigid motion.
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About this page
| Tag | 7JQS6VKFEZ |
|---|---|
| URI | m2://7JQS6VKFEZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A04 |
| Changed | 2 November 2026 |
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Used by
- Geodesic curvature
- Fáry–Milnor theorem
- Total curvature
- Fenchel's theorem
- Gage–Hamilton–Grayson theorem
- Torsion of a curve
- Fundamental theorem of space curves
- Evolute
- Osculating circle
- Four-vertex theorem
- Curve-shortening flow
- Frenet–Serret formulas