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  "body": "\n## Summary\n\nA Desarguesian plane is a [[projective plane|DANFNN8C4Y]] in which [[Desargues's theorem|5Z19Y02MME]] holds.\nThese are exactly the planes $\\mathbb{P}^2(D)$ built from a division ring $D$, so they are the planes that come from linear algebra.\nEvery finite Desarguesian plane is $\\mathbb{P}^2(\\F_q)$ for a finite field $\\F_q$.\nPlanes in which the theorem fails are called [[non-Desarguesian planes|HYE5FT4M34]].\n\n## Explanations\n\n### L1 human\n\nSome projective planes are built from numbers, by taking lines through the origin in a three-dimensional space.\nOthers are built by more exotic rules.\nDesargues's theorem about two triangles in perspective is the test that tells them apart: it holds exactly in the planes built from numbers.\nThe real projective plane and the Fano plane with $7$ points are Desarguesian.\n",
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