geometry-topology / Combinatorial Geometry
If $n$ planar points have no four concyclic, must some point determine $(1 - o(1))n$ distinct distances? Failing that, can one always force more than $(1/3 + c)n$?
Temporal state
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Append-only history
the strongest form is disproved via configurations where every point sees at most about 3n/4 distinct distances; the weaker improvement remains open
Research memory
If $n$ planar points have no four concyclic, must some point determine $(1 - o(1))n$ distinct distances? Failing that, can one always force more than $(1/3 + c)n$?
the strongest form is disproved via configurations where every point sees at most about 3n/4 distinct distances; the weaker improvement remains open
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