Other special cases of a square problem

TL;DR

This paper investigates specific cases of the open square problem concerning points with rational distances to vertices, extending previous partial results and contributing new special case proofs.

Contribution

We proved additional special cases of the square problem, building on Yang's prior work to advance understanding of rational distances in a unit square.

Findings

Identified new special cases where the point with rational distances exists.

Extended the class of squares for which the problem has a solution.

Provided mathematical proofs for these new cases.

Abstract

There exists "a square problem": in a unit square is there a point with four rational distances to the vertices? This problem is still regarded as unproved. Yang showed proofs for several special cases of the square problem. By the reference of Yang's researches, We have proved other special cases of this problem.