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

```@article{Bilyk2018OnTF,
title={On the Fejes T\'oth Problem about the Sum of Angles Between Lines},
author={D. Bilyk and Ryan Matzke},
journal={arXiv: Metric Geometry},
year={2018}
}```
• Published 2018
• Mathematics
• arXiv: Metric Geometry
In 1959 Fejes T\'oth posed a conjecture that the sum of pairwise non-obtuse angles between \$N\$ unit vectors in \$\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=1\$.
7 Citations

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Finite Normalized Tight Frames
• Mathematics, Computer Science