Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Fejes Tóth problem about the sum of angles between lines


Authors: Dmitriy Bilyk and Ryan W. Matzke
Journal: Proc. Amer. Math. Soc. 147 (2019), 51-59
MSC (2010): Primary 11K38, 52C35
DOI: https://doi.org/10.1090/proc/14263
Published electronically: October 18, 2018
MathSciNet review: 3876730
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse 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: $d=1$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11K38, 52C35

Retrieve articles in all journals with MSC (2010): 11K38, 52C35


Additional Information

Dmitriy Bilyk
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
MR Author ID: 757936
Email: dbilyk@math.umn.edu

Ryan W. Matzke
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
MR Author ID: 1115995
Email: matzk053@umn.edu

Received by editor(s): January 23, 2018
Published electronically: October 18, 2018
Additional Notes: This work is supported by the NSF grant DMS 1665007 (the first author) and the NSF Graduate Research Fellowship 00039202 (the second author)
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2018 American Mathematical Society