English

Optimally Packing a Large Square by Unit Squares

Algebraic Geometry 2026-02-03 v1

Abstract

We show that a large square of sidelength xx can be packed by unit squares in a manner so that the wasted space W(x)=O(x3/5)W(x) = O(x^{3/5}).

Cite

@article{arxiv.2602.01484,
  title  = {Optimally Packing a Large Square by Unit Squares},
  author = {Rory McClenagan},
  journal= {arXiv preprint arXiv:2602.01484},
  year   = {2026}
}

Comments

This work was extracted from the author's 2024 thesis available at https://unbc.arcabc.ca/dissertations-and-theses/15173 . Since then we have become aware of the 2025 paper arXiv:2508.04603 by Bui that shows a similar result by a different method

R2 v1 2026-07-01T09:30:37.914Z