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  "body": "\n## Summary\n\nA strictly convex set is a [[convex set|02AS45T3H9]] in which the open segment between any two distinct points lies in the [[interior|0RZH6W98HK]] of the set.\nIts boundary contains no flat piece: no nontrivial segment lies on the boundary.\nA normed space is a [[strictly convex space|GDTKW9KPH8]] exactly when its closed unit ball is a strictly convex set.\nStrict convexity gives uniqueness, for example of the point of a set where a nonzero linear function is largest.\n\n## Explanations\n\n### L1 human\n\nA disc is strictly convex: join two of its points and every point strictly between them is well inside the disc.\nA square is convex but not strictly convex.\nTwo points on the same side give a segment that runs along the edge and never enters the inside.\nSo strict convexity means that the boundary bulges outward everywhere and has no straight parts.\n",
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