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  "body": "\n## Summary\n\nAn extreme point of a convex set is a point of the set that lies strictly inside no segment between two other points of it.\nExtreme points are the corners of a convex set.\nThe [[Krein–Milman theorem|RSRAY0Q68S]] says that a compact convex set in a locally convex space is rebuilt from its extreme points by taking closed convex hulls.\nThey also matter in linear optimization, where a linear function on a compact convex set in $\\R^n$ reaches its maximum at an extreme point.\n\n## Explanations\n\n### L1 human\n\nThink of a convex shape, such as a filled polygon or a disc.\nA point is extreme if you cannot place it in the middle of a segment that stays in the shape and has other endpoints.\nFor a filled square the extreme points are the four corners.\nFor a filled disc every point of the boundary circle is extreme, and no inner point is.\n",
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