Unit-Area Triangles in Planar Sets of Large Measure

How large can a measurable $A \subseteq [0,R]^2$ be while avoiding the vertices of upward-oriented axis-aligned right triangles of area $1/2$? At most $O_c(R^2/(\log R)^c)$, with a matching-shaped lower bound construction.

Result

Proved

Status

Resolved

AI contribution

AI co-developed

Method

Argument

Field

Harmonic analysis

Posed by

Ronald Graham

Year posed

—

Years open

—

Solved

2026-05-28

Model

ChatGPT 5.4 Pro, Gemini 3.1 Pro

Vendor

OpenAI / Google

Collaborators

Aleksandar Bulj, Vjekoslav Kovac

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article