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  "body": "\n## Summary\n\nLet $K$ be a [[convex body|437FSG3419]] with the origin in its interior.\nIts intersection body is the star-shaped body whose radius in each direction $u$ is the volume of the central section of $K$ orthogonal to $u$.\nIt records all the hyperplane sections of $K$ through the origin in one geometric object.\nIntersection bodies were introduced by Lutwak, and they are the key to the answer of the [[Busemann–Petty problem|MV58A1F52E]].\n\n## Explanations\n\n### L1 human\n\nCut a solid through its centre with a flat knife held perpendicular to a direction $u$, and measure the area of the cut.\nDraw a point in direction $u$ at that distance from the centre.\nDoing this for every direction draws the boundary of the intersection body.\nFor a round ball every central cut is the same disc, so the intersection body of a ball is again a ball.\n",
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