Isosceles set $i(1)$
The size of the largest set of points in $\mathbb{R}^{1}$ in which every three points form an isosceles triangle.
Value: $3$ Verified lower bound
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$3$
Checked construction
isosceles-set-1-lower-3, submitted by daniel-munro, 2026-11-05 - Upper bound: None yet
Updates from the literature
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Lower bound: $3$
Trivial or easy according to the secondary source.
[via Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.] -
Upper bound: $3$
Trivial or easy according to the secondary source.
[via Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.]