This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and bynow classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book. A valuablesource of geometric problems User-friendly exposition and up-to-date bibliography provide insight into the latest research Useful as a textbook or a research monograph INDICE: Preface.- Part I.- Sphere Packings.- Finite Packings by Translatesof Convex Bodies.- Coverings by Homothetic Bodies - Illumination and Related Topics.- Coverings by Planks and Cylinders.- On the Volume of Finie Arrangements of Spheres.- Ball-Polyhedra as Interesctions of Congruent Balls.- Part II.-Selected Proofs on Sphere Packagings.- Selected Proofs on Finite Packagings of Translates of Convex Bodies.- Selected Proofs on Illumination and Related Topics.- Selected Proofs on Coverings by Planks and Cylinders.- Selected Proofs on the Kesner-Poulsen Conjecture.- Selected Proofs on Ball-Polyhedra.- References.
- ISBN: 978-1-4419-0599-4
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 166
- Fecha Publicación: 05/07/2010
- Nº Volúmenes: 1
- Idioma: Inglés