Details
Lagerungen
Arrangements in the Plane, on the Sphere, and in SpaceGrundlehren der mathematischen Wissenschaften, Band 360
139,09 € |
|
Verlag: | Springer |
Format: | |
Veröffentl.: | 27.03.2023 |
ISBN/EAN: | 9783031218002 |
Sprache: | englisch |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<p>The publication of the first edition of <i>Lagerungen in der Ebene, auf der Kugel und im Raum</i> 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 <i>Notes</i> to the 2nd edition.</p>The present version of <i>Lagerungen </i>makes this classic monograph available in English for the first time, with updated <i>Notes,</i> completed by extensive surveys of the state of the art. More precisely, this book consists of:<p></p><ol> <li>a corrected English translation of the original <i>Lagerungen,</i></li><li>the revised and updated <i>Notes</i> on the original text, </li><li>eight self-contained chapters surveying additional topics in detail.</li> </ol><p> </p><p>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.</p><br>
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.- 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.
<p>The publication of the first edition of <i>Lagerungen in der Ebene, auf der Kugel und im Raum</i> 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 <i>Notes</i> to the 2nd edition.</p>
<p>The present version of <i>Lagerungen </i>makes this classic monograph available in English for the first time, with updated <i>Notes,</i> completed by extensive surveys of the state of the art. More precisely, this book consists of:</p>
<ol> <li>a corrected English translation of the original <i>Lagerungen</i>,</li> <li>the revised and updated <i>Notes</i> on the original text, </li> <li>eight self-contained chapters surveying additional topics in detail.</li> </ol> <p>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.</p><p></p>
<p>The present version of <i>Lagerungen </i>makes this classic monograph available in English for the first time, with updated <i>Notes,</i> completed by extensive surveys of the state of the art. More precisely, this book consists of:</p>
<ol> <li>a corrected English translation of the original <i>Lagerungen</i>,</li> <li>the revised and updated <i>Notes</i> on the original text, </li> <li>eight self-contained chapters surveying additional topics in detail.</li> </ol> <p>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.</p><p></p>
First English translation of the classic monograph on packing and related problems Supplemented by extensive surveys on recent progress in the field, including sphere packings Includes a foreword by Tom Hales who solved the Kepler conjecture