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  "body": "\n## Summary\n\nA Finsler manifold is a [[smooth manifold|F45VQ47GPV]] with a smoothly varying, strongly convex [[norm|0V2WP9B1MF]]-like function on each tangent space.\nIt generalises a [[Riemannian manifold|7CBT4SM83Y]], where the length of a tangent vector comes from an inner product.\nLengths of curves, distances and geodesics are defined as in Riemannian geometry.\nBut the unit ball in each tangent space may be any smooth strongly convex body, not only an ellipsoid.\n\n## Explanations\n\n### L1 human\n\nIn Riemannian geometry, the set of tangent vectors of length one at a point is always an ellipse or an ellipsoid.\nFinsler geometry allows this unit set to be any smooth convex shape around the origin.\nThen the cost of moving can depend on the direction, as when walking with or against a wind.\nThe length need not even be symmetric: going one way along a path can cost less than coming back.\n",
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