Erdős problem 214

Let $S\subset \mathbb{R}^2$ be such that no two points in $S$ are distance $1$ apart. Must the complement of $S$ contain four points which form a unit square?

Sources

The source's own material, retained exactly.

6 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

214.lean

Retained formal statement5 of 6

The answer is yes, proved by Juhász [Ju79], who proved more generally that the complement of $S$ must contain a congruent copy of any set of four points.

FormalConjectures/ErdosProblems/214.leanErdos214.erdos_214.variants.juhasz1 lineExact file

1Erdos214.HasRedCopies 4

SolvedStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures6
statement retained
VibeMathed0
not observed here
PLBY Lean proofs1
no statement retained
Jayyhk Erdős Lean1
no statement retained
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki1
no statement retained
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 214.lean6