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  "body": "\n## Summary\n\nAn exposed point of a set $C$ is a point at which some linear function attains its maximum over $C$ and attains it nowhere else.\nGeometrically, some [[supporting hyperplane|K7N565NKCV]] touches $C$ at that point only.\nEvery exposed point is an [[extreme point|3MSGFJM2NX]], but not conversely.\nExposed points are the solutions found by linear optimisation over a convex set when the optimum is unique.\n\n## Explanations\n\n### L1 human\n\nA point of a shape is exposed if you can lay a flat wall against the shape so that it touches the shape at that point and nowhere else.\nThe corners of a square are exposed: a wall placed diagonally at a corner touches only that corner.\nEvery point of a circle is an exposed point of the disc.\nNow take a stadium, a rectangle with two half-discs glued on its short sides.\nThe points where a straight side meets a round end are extreme, but every supporting line there contains the whole straight side, so they are not exposed.\n",
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