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A region R is convex if, given any two points A and B in R, kA + (1-k)*B is also inside R for all k such that 0 ≤ k ≤ 1. In other words the whole of the line joining AB is inside the region R.
If there is even one pair of points A, B and just one value of k such that the relevant point is not in R, then R is not convex.
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