LEADER 04081nam 2200637 450 001 9910683348603321 005 20240202151847.0 010 $a9783031218002$b(electronic bk.) 010 $z9783031217999 024 7 $a10.1007/978-3-031-21800-2 035 $a(MiAaPQ)EBC7220681 035 $a(Au-PeEL)EBL7220681 035 $a(OCoLC)1374427989 035 $a(DE-He213)978-3-031-21800-2 035 $a(PPN)269093362 035 $a(EXLCZ)9926347416800041 100 $a20230730d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLagerungen $earrangements in the plane, on the sphere, and in space /$fLa?szlo? Fejes To?th, Ga?bor Fejes To?th, and Wlodzimierz Kuperberg 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (454 pages) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v360 311 08$aPrint version: Fejes Tóth, László Lagerungen Cham : Springer International Publishing AG,c2023 9783031217999 320 $aIncludes bibliographical references. 327 $aPart 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 -- 5. Packing in Space -- Part II. Notes and Additional Chapters to the English Edition -- 8. Notes -- 9. Finite Variations on the Isoperimetric Problem -- 10. Higher Dimensions -- 11. Ball Packings in Hyperbolic Space -- 12. Mutliple Arrangements -- 13. Neighbors -- 14. Packing and Covering Properties fo Sequences of Convex Bodies -- 15. Four Classic Problems -- 16. Miscellaneous Problems about Packing and Covering -- References for Part I -- References for Part II -- Name Index -- Subject Index. 330 $aThe publication of the first edition of Lagerungen in der Ebene, auf der Kugel und im Raum in 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László Fejes Tóth in his Notes to the 2nd edition. The present version of Lagerungen makes this classic monograph available in English for the first time, with updated Notes, completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original Lagerungen, the revised and updated Notes on the original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v360 606 $aConvex surfaces 606 $aPolyhedra 606 $aSphere 606 $aSuperfícies convexes$2thub 606 $aPoliedres$2thub 606 $aEsfera$2thub 608 $aLlibres electrònics$2thub 615 0$aConvex surfaces. 615 0$aPolyhedra. 615 0$aSphere. 615 7$aSuperfícies convexes 615 7$aPoliedres 615 7$aEsfera 676 $a929.605 700 $aFejes To?th$b La?szlo?$0424017 702 $aFejes To?th$b G. 702 $aKuperberg$b Wlodzimierz 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910683348603321 996 $aLagerungen$93085160 997 $aUNINA