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  "body": "\n## Summary\n\nThe Gaussian curvature of a surface at a point is the product of its two [[principal curvatures|FA8QE1SGP4]].\nIt is positive at dome-like points, negative at saddle-like points, and zero on surfaces that can be unrolled flat.\nBy Gauss's Theorema Egregium it depends only on the first fundamental form, so it can be measured from inside the surface.\n\n## Explanations\n\n### L1 human\n\nTry to flatten an orange peel on a table: it tears, because the sphere has positive Gaussian curvature.\nA piece of a cylinder, like a rolled sheet of paper, flattens without stretching, because its Gaussian curvature is zero.\nA saddle or a potato crisp has negative Gaussian curvature: it curves up one way and down the other.\nA sphere of radius $r$ has Gaussian curvature $1/r^2$ at every point.\n",
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