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  "body": "\n## Summary\n\nA non-Euclidean geometry is a geometry that keeps the other basic assumptions of [[Euclidean geometry|KRZD96GSVC]] but drops the [[parallel postulate|2PC3XY0PYZ]].\nThe two classical ones are [[hyperbolic geometry|GN4N94GQ0Z]], where a line has many parallels through an outside point, and [[elliptic geometry|H5GB19W2H3]], where it has none.\nTheir discovery showed that the parallel postulate cannot be proved from the other axioms.\nThey also became models for curved space in differential geometry and physics.\n\n## Explanations\n\n### L1 human\n\nIn school geometry, through a point off a line there is exactly one line that never meets it.\nFor two thousand years people tried to prove this from simpler rules and failed.\nNon-Euclidean geometries are consistent worlds where this rule is false.\nOn a sphere, where great circles play the role of lines, any two lines meet, and the angles of a triangle add up to more than $180^\\circ$.\n",
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