/-
Copyright 2026 The Formal Conjectures Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-/
import FormalConjecturesUtil
import FormalConjectures.ErdosProblems.«507»
open Erdos507 Filter Topology
namespace Green77
Given $n$ points in the unit disc, must there be a triangle of area at most $n^{-2+o(1)}$ determined by them?
@[category research open, AMS 5 52]
theorem green_77 :
answer(sorry) ↔
∃ (o : ℕ → ℝ), Tendsto o atTop (𝓝 0) ∧
α ≪ fun n ↦ n ^ (-2 + o n) := ⊢ True ↔ ∃ o, Tendsto o atTop (𝓝 0) ∧ α =O[atTop] fun n => ↑n ^ (-2 + o n)
All goals completed! 🐙
end Green77