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For questions involving the concept of convexity

2 votes
Accepted

Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equali...

Here is a sketch of an answer that involves the squared Euclidean distances between the four points $A,B,C,D$ (and only the squared ones, not a mixture between squared and non-squared distances.) Sup …
2 votes

Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equali...

No. (This was an answer to a previous, not entirely clear version of the problem.) Take an equilateral triangle ABC of side length 1, plus the midpoint D of the side AC. By pushing D slightly in or ou …
Günter Rote's user avatar
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