Convex and discrete geometry
$4,989 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-99Command line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«99»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos99.erdos_99" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ᶠ (n : ℕ) in Filter.atTop,
∀ (A : Finset (EuclideanSpace ℝ (Fin 2))),
A.card = n →
Erdos99.HasMinDist1 A →
IsMinOn (fun B => Metric.diam ↑B) {B | B.card = n ∧ Erdos99.HasMinDist1 B} A →
∃ p ∈ A, ∃ q ∈ A, ∃ r ∈ A, Erdos99.FormsEquilateralTriangle p q rOriginal conjecture source: FormalConjectures/ErdosProblems/99.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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