Erdős problem 503 · problems.science

What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$ , $y$ , $z$ from $A$ , at least two of the distances $|x - y|$ , $|y - z|$ , $|x - z|$ are equal.

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

503.lean

Retained formal statement4 of 5

When $n = 3$ , the answer is 8 (due to Croft [Cr62]).

[Cr62] Croft, H. T., $9$ -point and $7$ -point configurations in $3$ -space. Proc. London Math. Soc. (3) (1962), 400-424.

FormalConjectures/ErdosProblems/503.leanErdos503.erdos_503.variants.R31 lineExact file

1IsGreatest {x | ∃ A, ∃ (_ : A.IsIsosceles), A.ncard = x} 8

SolvedStatement only, no proof

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