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  "body": "\n## Summary\n\nAffine differential geometry studies curves and surfaces through the properties that do not change under volume-preserving affine maps of space.\nLengths and angles are not preserved by such maps, so the Euclidean curvature of a curve or surface is not an invariant here.\nInstead the theory builds its own invariants.\nExamples are the affine arc length of a curve and the affine normal and Blaschke metric of a hypersurface.\nIt is an instance of the idea that each group of transformations has its own geometry.\n\n## Explanations\n\n### L1 human\n\nStretch a drawing in one direction and squeeze it in another so that areas stay the same.\nCircles turn into ellipses, and lengths change, but some features of curves survive.\nAffine differential geometry studies exactly these surviving features.\nFor example, every parabola looks the same as every other parabola from this point of view, just as every circle looks the same in Euclidean geometry up to size.\n",
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