OpenAI reports a power improvement for Heilbronn triangles
- Mathematics
There are fixed constants η,c>0 such that, for every sufficiently large n, n points can be placed in the unit square with every triangle of area at least c n^{-2+η}.
OpenAI reports a power improvement for Heilbronn triangles
- Mathematics
There are fixed constants η,c>0 such that, for every sufficiently large n, n points can be placed in the unit square with every triangle of area at least c n^{-2+η}.
Curated contributions 1
Understand the problem ↓Understanding the problem
Read the background
There are fixed constants η,c>0 such that, for every sufficiently large n, n points can be placed in the unit square with every triangle of area at least c n^{-2+η}.
Why it matters
If correct, disproves the nearly n^{-2} upper-bound formulation of Heilbronn’s triangle problem.
What counts as progress
Can the smallest triangle area for n points exceed n^{-2} by a fixed power for all large n?
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