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  "body": "\n## Summary\n\nA Moufang plane is a [[projective plane|DANFNN8C4Y]] in which the little Desargues theorem holds.\nThis is the special case of [[Desargues's theorem|5Z19Y02MME]] where the centre of perspective lies on the axis.\nEquivalently, every line is a translation line: the plane has as many elations with that axis as possible.\nMoufang planes are exactly the planes coordinatized by alternative division rings.\nEvery [[Desarguesian plane|HPX85PA8NX]] is a Moufang plane, and the [[octonionic projective plane|S26GYRVDR5]] is a Moufang plane that is not Desarguesian.\n\n## Explanations\n\n### L1 human\n\nDesargues's theorem says that two triangles in perspective from a point are also in perspective from a line.\nA Moufang plane is only asked to satisfy this when the point lies on the line.\nThis weaker rule still gives the plane many symmetries.\nIn coordinates, it allows multiplication that is not associative, as long as it is alternative, as for the octonions.\n",
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