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  "body": "\n## Summary\n\nA rational surface is an [[algebraic surface|KFTECAATKG]] that is birational to the projective plane.\nIt is the two-dimensional case of a [[rational variety|XV4K9GREJ9]].\nRational surfaces include the projective plane, the quadric $\\mathbb{P}^1 \\times \\mathbb{P}^1$, the Hirzebruch surfaces, the blow-ups of the plane in points, and all smooth cubic surfaces.\nThey are the surfaces whose points can be parametrized, outside a lower-dimensional set, by two free parameters.\n\n## Explanations\n\n### L1 human\n\nA surface is rational when its points can be described by two independent parameters through rational functions, with an inverse that is also given by rational functions.\nFor instance, the sphere $x^2 + y^2 + z^2 = 1$ can be parametrized by stereographic projection from a point, so it is rational.\nTwo rational surfaces can look very different, but they agree with the plane after removing some curves.\n",
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