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  "body": "\n## Summary\n\nA Laguerre plane is an incidence structure of points and circles with a parallelism of points.\nIt is modelled on the plane sections of a circular cylinder.\nThree pairwise non-parallel points lie on exactly one circle, and each circle meets each parallel class in exactly one point.\nIt is one of the three kinds of [[Benz plane|BG5A4CB6NB]].\n\n## Explanations\n\n### L1 human\n\nTake a round cylinder and cut it with planes that are not parallel to its axis; the cuts are ellipses, called circles here.\nTwo points on the same vertical line of the cylinder are called parallel, and no circle passes through both.\nThrough three points with no two parallel there is exactly one such circle.\nA flat picture of the same geometry uses parabolas $y = ax^2 + bx + c$ in the plane, with vertical lines as parallel classes.\n",
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