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  "body": "\n## Summary\n\nThe torsion of a space curve measures how fast the curve twists out of its osculating plane.\nThis is the plane that best fits the curve at a point.\nA plane curve has torsion $0$ everywhere.\nWith [[curvature|7JQS6VKFEZ]], torsion appears in the Frenet–Serret formulas and determines a space curve up to a rigid motion.\n\n## Explanations\n\n### L1 human\n\nCurvature tells how a curve bends inside a plane, and torsion tells how that plane itself turns.\nPicture the thread of a screw: it bends around the axis and also climbs, so it leaves every plane.\nA circle lies flat in one plane and has torsion $0$.\nThe helix $t \\mapsto (\\cos t, \\sin t, t)$ climbs at a steady rate and has constant torsion $1/2$.\n",
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