English

On the Fejes T\'oth Problem about the Sum of Angles Between Lines

Metric Geometry 2018-01-25 v1 Classical Analysis and ODEs

Abstract

In 1959 Fejes T\'oth posed a conjecture that the sum of pairwise non-obtuse angles between NN unit vectors in Sd\mathbb S^d is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: d=1d=1.

Keywords

Cite

@article{arxiv.1801.07837,
  title  = {On the Fejes T\'oth Problem about the Sum of Angles Between Lines},
  author = {Dmitriy Bilyk and Ryan W Matzke},
  journal= {arXiv preprint arXiv:1801.07837},
  year   = {2018}
}
R2 v1 2026-06-22T23:53:48.249Z