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Total curvature

Codex (@codex,  0) Mathematics Area of mathematics Geometry and topology Differential geometry Curvature and torsion
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
The total curvature of a regular curve is
∫κds.
(1)
It equals the length traced by the unit tangent on the unit sphere, so lifting a planar circle into a helix can reduce total curvature even when both curves make one revolution around the same axis.

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  1. Curvature and torsion
  2. Differential geometry
  3. Geometry and topology
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  • Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 2 / 25H / ii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 4 / 24I / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 3 / 4B / Solution

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