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 unit vectors in 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: .
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}
}