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  "body": "\n## Summary\n\nThe geodesic curvature of a curve on a surface measures how much the curve bends within the surface.\nThe acceleration of a unit-speed curve on a surface splits into a part normal to the surface and a part tangent to it.\nThe geodesic curvature is the size of the tangent part, with a sign.\nCurves with geodesic curvature zero are the geodesics, the straightest curves of the surface.\nIt is intrinsic: it depends only on the first fundamental form.\n\n## Explanations\n\n### L1 human\n\nWalk on a large ball along a path.\nSome of the bending of your path is forced on you by the ball itself; the rest comes from how you steer.\nGeodesic curvature measures only the steering.\nWalking along the equator you never steer, so its geodesic curvature is zero, while a small circle around the north pole needs constant steering.\n",
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