On particular examples of planar integral point sets and their classification

TL;DR

This paper explores the classification of planar integral point sets, which are non-collinear points in a plane with all pairwise distances integral, and provides new examples beyond existing classifications.

Contribution

It offers a new classification framework for planar integral point sets and presents examples not previously covered by existing methods.

Findings

New examples of planar integral point sets identified

Existing classifications are incomplete or limited

Proposed a broader classification approach

Abstract

A planar integral point set is a set of non-collinear points in plane such that for any pair of the points the Euclidean distance between the points is integral. We discuss the classification of planar integral point sets and provide examples of sets that are not covered by the existent classification.