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  "body": "\n## Summary\n\nSystolic geometry studies the systole of a Riemannian manifold, the length of its shortest closed curve that cannot be shrunk to a point.\nIts main questions compare the systole with the volume of the manifold.\nTypical results say that a manifold with a long systole must have a large volume, as in [[Loewner's torus inequality|1Y9X1YW6GH]] and [[Gromov's systolic inequality|HB2K72PSZ6]].\nThe field links Riemannian geometry with topology and with the geometry of numbers.\n\n## Explanations\n\n### L1 human\n\nOn a doughnut surface some loops cannot be pulled tight to a point, such as a loop around the hole.\nThe systole is the length of the shortest such loop.\nIf all these loops are long, the surface must be large: it cannot have small area.\nFor a flat square torus made from a unit square, the systole is $1$ and the area is $1$.\nSystolic geometry asks how small the area can be once the systole is fixed.\n",
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