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  "body": "\n## Summary\n\nThe second fundamental form of a surface in $\\R^3$ is a quadratic form on each tangent plane.\nIt measures how the surface bends away from that plane.\nIn a local parametrisation it is given by three functions, often written $e$, $f$, $g$ or $L$, $M$, $N$.\nTogether with the [[first fundamental form|MAJ3DH7MZS]] it determines the principal, Gaussian and mean curvatures.\n\n## Explanations\n\n### L1 human\n\nPut a flat sheet of glass on a surface so that it touches at one point.\nNear that point the surface pulls away from the glass, faster in some directions and slower in others.\nThe second fundamental form records, for each direction, how fast the surface pulls away.\nOn a sphere it pulls away equally in all directions, and on a saddle it rises in some directions and falls in others.\n",
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