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  "body": "\n## Summary\n\nAn umbilical point, or umbilic, of a surface is a point where the two [[principal curvatures|FA8QE1SGP4]] are equal.\nThere the surface bends by the same amount in every direction, like a sphere or a plane.\nEvery point of a sphere or a plane is umbilical.\nConversely, a connected surface made only of umbilical points is a piece of a sphere or of a plane.\n\n## Explanations\n\n### L1 human\n\nAt most points of a surface there is a direction of strongest bending and a direction of weakest bending.\nAt an umbilical point there is no preferred direction: the surface looks the same in every direction, up to second order.\nOn a ball every point is like this.\nAn egg-shaped ellipsoid with three different axes has exactly four such special points.\n",
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