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  "body": "\n## Summary\n\nThe Erlangen program is a view of geometry that Felix Klein stated in 1872.\nIn it, a geometry is the study of the properties of a space that are invariant under a given [[group|G5S1M9]] of transformations.\nEuclidean, affine and projective geometry then differ only in their groups: the [[Euclidean group|0H3YY8CPKH]], the [[affine group|G6GMSEZDB1]] and the projective group.\nA larger group has fewer invariants, so projective geometry has fewer theorems than affine geometry, which has fewer than [[Euclidean geometry|KRZD96GSVC]].\n\n## Explanations\n\n### L1 human\n\nKlein asked what makes a fact \"geometric\".\nHis answer: a fact is geometric if it survives the moves that the geometry allows.\nIn Euclidean geometry the moves are rigid motions, so lengths and angles count.\nIn affine geometry the moves may also stretch and shear, so lengths are lost, but parallel lines stay parallel and midpoints stay midpoints.\n",
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