ProbXiv
sign in
Problem archiveProblem record

Unit-Area Triangles in Planar Sets of Large Measure

Analysis · posed by Ronald Graham · solved

1 comment

Statement

How large can a measurable A⊆[0,R]2A \subseteq [0,R]^2 be while avoiding the vertices of upward-oriented axis-aligned right triangles of area 1/21/2? At most Oc(R2/(log⁡R)c)O_c(R^2/(\log R)^c), with a matching-shaped lower bound construction.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Aleksandar Bulj and Vjekoslav Kovac, using ChatGPT 5.4 Pro, Gemini 3.1 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The AI usage declaration names two distinct contributions: ChatGPT 5.4 Pro constructed the example giving the lower bound, and was also used to clarify a cryptic remark of Graham and reconstruct its intended proof. Gemini drew a figure. The authors state the ideas, proofs and writing are theirs.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.