Strange Phenomena in Convex and Discrete Geometry

Zong, Chuanming; James J. Dudziak (editor)

ISBN 10: 0387947345 / ISBN 13: 9780387947341

Verlag: Springer, New York, Berlin, Etc., 1996

Beschreibung

With illustrations. Light shelfwear. ; "Strange Phenomena in Convex and Discrete Geometry" by Chuanming Zong explores intriguing and often counterintuitive properties and problems in the field of geometry. This book examines a variety of unusual phenomena within the context of convex and discrete structures, which are areas known for their complex and sometimes unexpected behavior in mathematical configurations. Zong's work is particularly focused on providing insights into the unique behaviors and characteristics that emerge from the geometric arrangement of figures and points. The book details several key topics, such as the illumination problem, where the challenge is to determine the minimum number of light sources needed to illuminate the entire interior of a given shape; and the Kneser-Poulsen conjecture, which deals with the optimal way to pack spheres so that the distance between their centers is minimized. Throughout the text, Zong uses clear, precise language and provides mathematical proofs to explore these phenomena, making complex topics accessible to those with a solid foundation in mathematics. The book serves both as a scholarly resource for mathematicians and as an intriguing exploration for advanced students engaged in studies of geometric analysis, offering a deep dive into how simple geometric principles can lead to surprising and enlightening conclusions.; Universitext; Octavo; viii, 159 pages.

Bestandsnummer des Verkäufers LCB60987

Bibliografische Details

• Titel: Strange Phenomena in Convex and Discrete Geometry
• Verlag: Springer, New York, Berlin, Etc.
• Erscheinungsjahr: 1996
• Sprache: Englisch
• ISBN-10: 0387947345
• ISBN-13: 9780387947341
• Einband: Original decorated wrappers
• Auflage: First Edition; First Impression.
• Zustand: Fine
• Zustand des Schutzumschlags: No Dust Jacket

Über diesen Titel

Inhaltsangabe

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

Von der hinteren Coverseite

This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphere-packing problem (how can one arrange m nonoverlapping congruent spheres in an n-dimensional Euclidean space to minimize the volume or surface area of their convex hull?) - as well as their (at times astonishing) answers. Though covering some of the most recent developments in the field, the book is self-contained, and can be understood by any trained mathematician.