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  "body": "\n## Summary\n\nIncidence geometry is the part of geometry that studies points, lines and the relation \"lies on\", and nothing else.\nIts objects are [[incidence structures|FGKNAFNHA3]] that satisfy axioms such as \"two points lie on exactly one line\".\n[[Affine planes|EC7XT2ZM5S]], [[projective planes|DANFNN8C4Y]] and finite geometries are its main examples.\nIt asks which configurations the axioms force.\nIt also asks which algebra, such as a field or a division ring, can be rebuilt from the points and lines alone.\n\n## Explanations\n\n### L1 human\n\nOrdinary geometry talks about lengths and angles.\nIncidence geometry throws these away and keeps only the question of which points lie on which lines.\nSurprisingly much survives: theorems such as those of Desargues and Pappus only speak about points being on lines.\nIt also allows small finite worlds, such as a geometry with $7$ points and $7$ lines, that behave like the plane in this respect.\n",
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