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  "body": "\n## Summary\n\nA family of points is convexly independent if no point of the family lies in the [[convex hull|0FQSDC2EQ2]] of the other points.\nA set of points with this property is said to be in convex position.\nThen every point of the set is an [[extreme point|3MSGFJM2NX]] of its convex hull.\nThe notion is the convex analogue of linear and affine independence, and it is central in problems such as the Erdős–Szekeres problem on convex polygons.\n\n## Explanations\n\n### L1 human\n\nPoints are in convex position when each of them is a corner of the shape they span.\nStretch a rubber band around the points: every point must touch the band at a corner.\nThe four corners of a square are convexly independent.\nIf one adds the center of the square, the new set is not, because the center lies inside the square spanned by the corners.\n",
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