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  "body": "\n## Summary\n\nA projective plane is an [[incidence structure|FGKNAFNHA3]] in which two points lie on exactly one line and two lines meet in exactly one point.\nIt is the plane of perspective drawing, where parallel lines meet at a point at infinity.\nThe real projective plane and the planes $\\mathbb{P}^2(k)$ over fields are examples, and there are also planes that come from no field.\nFinite projective planes are central objects of combinatorics.\n\n## Explanations\n\n### L1 human\n\nIn a perspective drawing, railway tracks meet at a point on the horizon.\nA projective plane makes this a rule: any two lines meet, and the horizon becomes a line like the others.\nThrough two points there is still exactly one line.\nThe smallest projective plane, the Fano plane, has $7$ points and $7$ lines, with $3$ points on each line and $3$ lines through each point.\n",
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