Lagerungen : arrangements in the plane, on the sphere, and in space / László Fejes Tóth, Gábor Fejes Tóth, Włodzimierz Kuperberg.

Format:

Book

Author/Creator:

Fejes Tóth, L., author.

Fejes Tóth, G., author.

Kuperberg, Włodzimierz, author.

Series:

Grundlehren der mathematischen Wissenschaften ; 360.

Grundlehren der mathematischen Wissenschaften, 0072-7830 ; Volume 360

Standardized Title:

Lagerungen in der Ebene, auf der Kugel und im Raum. English

Language:

English

German

Subjects (All):

Polyhedra.

Convex surfaces.

Sphere.

Physical Description:

xxiv, 442 pages : illustrations, color portrait ; 25 cm

Place of Publication:

Cham : Springer, [2023]

Summary:

"The publication of the first edition of 'Lagerungen in der Ebene, auf der Kugel und im Raum' in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen; the revised and updated Notes on the original text; eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come" -- Backside cover.

Contents:

Part I. Lagerungen

Arrangements in the plane, on the sphere, and in space : 1. Some theorems from elementary geometry

2. Theorems from the theory of convex bodies

3. Problems on packing and covering in the plane

4. Efficiency of packings and coverings with a sequence of convex disks

5. Extremal properties of regular polyhedra

6. Irregular packing on the sphere

7. Packing in space

Part II. Notes and additional chapters to the English edition : 8. Notes / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg

9. Finite variations on the isoperimetric problem / G. Fejes Tóth

10. Higher dimensions / G. Fejes Tóth

11. Ball packings in hyperbolic space / G. Fejes Tóth, L. Fejes Tóth and W.. Kuperberg

12. Multiple arrangements / G. Fejes Tóth

13. Neighbors / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg

14. Packing and covering properties of sequences of convex bodies / G. Fejes Tóth

15. Four classic problems / G. Fejes Tóth and W. Kuperberg

16. Miscellaneous problems about packing and covering / G. Fejes Tóth, L. Fejes Tóth and W. Kuperberg

References for Part I

References for Part II

Name index

Subject index.

Notes:

Includes bibliographical references (pages 337-420) and indexes.

ISBN:

9783031217999

3031217993

OCLC:

1348378333