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  "body": "\n## Summary\n\nA regular surface is a subset of $\\R^3$ that looks, near each of its points, like a smoothly bent piece of the plane.\nNear each point it is the image of a smooth injective map from an open set of the plane, with linearly independent partial derivatives.\nRegular surfaces are the setting of the classical differential geometry of surfaces: tangent planes, fundamental forms and curvatures are defined on them.\n\n## Explanations\n\n### L1 human\n\nThink of the skin of a ball, or the surface of a doughnut.\nIf you zoom in at any point, you see something that is almost a flat sheet, bent but without folds, creases or sharp tips.\nA regular surface is a shape in space with this property at every point.\nThe tip of a cone is a sharp point, so a cone with its tip is not a regular surface, but the sphere is.\n",
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