Balancing pairs of adjacent slices of cake

David Bevan

Balancing pairs of adjacent slices of cake

Combinatorics 2026-07-06 v1

Authors: David Bevan

Abstract

After $n$ radial cuts of a circular cake, it is divided into $n$ slices. Call an adjacent pair of slices a portion. We exhibit an infinite sequence of cuts such that the ratio between the maximum and minimum sizes of a portion never exceeds 1.755. This improves on the trivial upper bound of 2, disproving a conjecture of Korsky.

Keywords

cake cutting adjacent slices balancing ratio conjecture

Cite

@article{arxiv.2607.05330,
  title  = {Balancing pairs of adjacent slices of cake},
  author = {David Bevan},
  journal= {arXiv preprint arXiv:2607.05330},
  year   = {2026}
}

Comments

3 pages