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  "body": "\n## Summary\n\nA developable surface is a surface in space whose Gaussian curvature is zero at every point.\nSuch a surface can be flattened onto a plane, at least locally, without stretching or tearing.\nCylinders, cones and the surfaces swept by the tangent lines of a space curve are the basic examples.\nThey matter in practice because they are the shapes one can bend out of a flat sheet of paper or metal.\n\n## Explanations\n\n### L1 human\n\nRoll a sheet of paper into a tube or a cone: you get a developable surface.\nNo length on the paper changes when you do this, so you can unroll it flat again.\nA sphere is not developable, which is why every flat map of the Earth distorts some distances.\nThe number that decides this is the Gaussian curvature: it is zero on a cylinder and positive on a sphere.\n",
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