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Five Essays on the Geometry of László Fejes Tóth

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New Trends in Intuitive Geometry

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 27))

Abstract

In this paper we consider the following topics related to results of László Fejes Tóth: (1) The Tammes problem and Fejes Tóth’s bound on circle packings; (2) Fejes Tóth’s problem on maximizing the minimum distance between antipodal pairs of points on the sphere; (3) Fejes Tóth’s problem on the maximum kissing number of packings on the sphere; (4) The Fejes Tóth–Sachs problem on the one-sided kissing numbers; (5) Fejes Tóth’s papers on the isoperimetric problem for polyhedra.

This research is partially supported by the NSF grant DMS-1400876 and the RFBR grant 15-01-99563.

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Notes

  1. 1.

    Actually, Danzer’s paper [15] is the English translation of his Habilitationsschrift “Endliche Punktmengen auf der 2-sphäre mit möglichst großem Minimalabstand”. Universität Göthingen, 1963.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, One West University Boulevard, Brownsville, TX, 78520, USA

    Oleg R. Musin

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  1. Oleg R. Musin
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Correspondence to Oleg R. Musin .

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Editors and Affiliations

  1. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gergely Ambrus

  2. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Imre Bárány

  3. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Károly J. Böröczky

  4. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gábor Fejes Tóth

  5. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    János Pach

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Musin, O.R. (2018). Five Essays on the Geometry of László Fejes Tóth. In: Ambrus, G., Bárány, I., Böröczky, K., Fejes Tóth, G., Pach, J. (eds) New Trends in Intuitive Geometry. Bolyai Society Mathematical Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57413-3_13

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