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  "body": "\n## Summary\n\nEuclidean geometry is the geometry of the [[Euclidean plane|0XW7V9ZZ05]] and of [[Euclidean space|0XPR1E85W0]]: the study of points, lines, distances and angles in a flat space.\nIt can be built synthetically from axioms, as in [[Euclid's Elements|83WHDAV68J]] and [[Hilbert's axioms|KM1FB8XZ2R]], or analytically with coordinates in $\\R^n$.\nIts characteristic axiom is the [[parallel postulate|2PC3XY0PYZ]]; dropping it leads to [[absolute geometry|VKFPCSRNDH]] and to [[non-Euclidean geometry|SPCYMFN5V2]].\n\n## Explanations\n\n### L1 human\n\nEuclidean geometry is the geometry of a flat sheet of paper that goes on forever.\nStraight lines, circles, triangles and their measures are its objects.\nThrough a point outside a line there is exactly one line parallel to it, and the angles of a triangle add up to $180^\\circ$.\nFor example, a triangle with sides $3$, $4$ and $5$ has a right angle, by the [[Pythagorean theorem|0VP3A1290K]].\n",
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