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  "body": "\n## Summary\n\nA Möbius plane is an incidence structure of points and circles that behaves like the circles on a sphere.\nAny three points lie on exactly one circle, and circles can touch.\nThe classical example is the plane with one point at infinity, where circles and lines through infinity are the circles.\nMöbius planes are one of the three kinds of [[Benz plane|BG5A4CB6NB]], and they give the axiomatic setting of [[inversive geometry|HFBW3SXQVM]].\n\n## Explanations\n\n### L1 human\n\nOn a sphere, any three points lie on exactly one circle.\nTwo circles can meet in two points, in no point, or touch in one point.\nA Möbius plane keeps exactly these facts as axioms and forgets the rest.\nStereographic projection turns the sphere into the plane plus one point at infinity, and circles through that point become straight lines.\n",
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