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  "body": "\n## Summary\n\nThe curvature of a curve measures how fast its direction turns per unit of length travelled.\nFor a unit-speed curve it is the length of the acceleration vector.\nA straight line has curvature $0$ and a circle of radius $r$ has curvature $1/r$.\nCurvature, together with torsion, determines a space curve up to a rigid motion.\n\n## Explanations\n\n### L1 human\n\nDrive a car along a road at constant speed and watch the steering wheel.\nOn a straight road the wheel is centred, and on a sharp bend it is turned far.\nCurvature is the number that records how far the wheel is turned at each point of the road.\nA circle of radius $2$ metres has curvature $1/2$ per metre at every point, and a larger circle bends more gently and has smaller curvature.\n",
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