Least Action Principle of Crystal Formation of Defense Packing Type and Kepler's Conjecture.

HSIANG, Wu Yi

ISBN 10: 9810246706 / ISBN 13: 9789810246709

Published by World Scientific, New Jersey, 2001

About this Item

New Jersey, World Scientific (2001). Some figs. XXI, 402 p. Hardbound. Nankai Tracts in Mathematics, 3.- Dedication by the author on flyleaf.- Like new.

Seller Inventory # 96341

Bibliographic Details

• Title: Least Action Principle of Crystal Formation of Defense Packing Type and Kepler's Conjecture.
• Publisher: World Scientific, New Jersey
• Publication Date: 2001
• Language: English
• ISBN 10: 9810246706
• ISBN 13: 9789810246709
• Binding: Hardcover
• Condition: Wie neu

About this title

Synopsis

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of B/√18. In 1611, Johannes Kepler had already "conjectured" that B/√18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/√18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.

Review

The book presents an expostition of the ideas suggested by W Y Hsiang to prove this interesting and difficult conjecture. -- Mathematics Abstracts