Least Action Principle of Crystal Formation of Dense Packing Type and the Proof of Kepler's Conjecture

By: Wu-yi Hsiang, Weiping Zhang (Editor)

Write A Review

Hardcover | 1 December 2000

At a Glance

Hardcover
424 Pages

Dimensions(cm)
21.59 x 15.88 x 3.18

Hardcover

RRP $275.99

$248.75

10%OFF

or 4 interest-free payments of $62.19 with

or

Ships in 15 to 25 business days

This work provides proof of Kepler's conjecture about optimal density, and establishes the least action principle, which states that the hexagonal dense packings in crystals are the geometric consequence of optimization of density.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Differential & Riemannian Geometry

Riemannian Geometry and Geometric Analysis : Universitext - Jurgen Jost

$29.75

Geometric Orbifold Cohomology

Hardcover

RRP $263.00

$262.75

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Volume 120

Paperback

RRP $203.95

$159.75

22%
OFF

Geometry, Dynamics, and Rigidity - Amie Wilkinson

$455.75

10%
OFF

Differential Geometric Methods in Theoretical Physics : Twentieth International Conference : Twentieth International Conference - Sultan Catto

$123.75

10%
OFF

Geometry in Partial Differential Equations

Hardcover

RRP $352.99

$317.75

10%
OFF

Geometry and Topology of Submanifolds VI

Hardcover

$284.99

Harmonic Maps

Hardcover

RRP $293.99

$264.75

10%
OFF

Concise Complex Analysis

Hardcover

RRP $124.99

$112.75

10%
OFF

Selected Papers of Wilhelm P. A. Klingenberg

SERIES IN PURE MATHEMATICS

Hardcover

RRP $354.99

$319.75

10%
OFF

Foreword
Acknowledgment
List of Symbols
Introduction	p. 1
Sphere Packings and the Sphere Packing Problem	p. 1
Kepler's Conjecture on Sphere Packings	p. 4
Density of Finite Packings without a Container and the Least Action Principle of Crystal Formation	p. 6
Locally Averaged Density and the Intrinsic Density of the Second Kind	p. 13
Main Theorems on Sphere Packings	p. 14
The Basics of Euclidean and Spherical Geometries and a New Proof of the Problem of Thirteen Spheres	p. 19
Vector Algebra and Basic Spherical Geometry	p. 20
Spherical Configurations, Area Estimates and a New Proof of the Impossibility of Thirteen Touching Neighbors	p. 61
Circle Packings and Sphere Packings	p. 83
The Problem of Circle Packings	p. 83
Sphere Packings and Crystal Formations, Kepler's Conjecture and a Least Action Principle of Crystal Formation	p. 89
Some Basic Ideas and Crucial Understanding which the Proofs of the Major Theorems are Based	p. 106
Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells	p. 123
Basic Geometry of Local Packings and Local Cells	p. 123
Technique of Volume Estimation of the Core Part	p. 138
Volume Estimation of a Rectilinear Slab	p. 164
Volume Estimation of Local Cells	p. 187
Estimates of Total Buckling Height	p. 201
The Correlation Between Buckling Heights and Area Estimates	p. 204
Area Estimates of Star Configurations	p. 215
Estimation of Total Buckling Height	p. 225
The Proof of the Dodecahedron Conjecture	p. 235
The Proof of Case 1: m = 12	p. 236
The Proof of Case 2: m [is equal to or less then] 11	p. 237
The Proof of Case 3: 13 [is equal to or less then] m [is equal to or less then] 15	p. 238
Geometry of Type I Configurations and Local Extensions	p. 239
Geometry of Type I Local Packings and Type I Configurations	p. 241
Geometry of Local Extension	p. 300
The Proof of Main Theorem I	p. 327
The Proof of Main Theorem I for Core Packings with at Least Thirteen Close Neighbors	p. 329
The Proof of Main Theorem I for Core Packings with at Most Twelve Close Neighbors	p. 332
Retrospects and Prospects	p. 383
Retrospects	p. 383
Prospects	p. 387
References	p. 397
Index	p. 401
Table of Contents provided by Blackwell. All Rights Reserved.

Least Action Principle of Crystal Formation of Dense Packing Type and the Proof of Kepler's Conjecture

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Differential & Riemannian Geometry

Riemannian Geometry and Geometric Analysis

Universitext

Cartoon Guide to Calculus

Cartoon Guide Series

Geometric Orbifold Cohomology

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Volume 120

Geometry, Dynamics, and Rigidity

Geometry of Frameworks

Compact Textbooks in Mathematics

Complex Geometry and Mathematical Physics

Classical and Quantum Singularities of Space-Times (Book III-B)

Geometry on Manifolds

Riemannian Metrics, Symplectic Forms, Contact Structures

Analysis on Manifolds

An Introduction to Manifolds

Universitext

Complex Singularity Theory and Cauchy-Riemann Geometry

Springer Monographs in Mathematics

Calculus On Manifolds

A Modern Approach To Classical Theorems Of Advanced Calculus

Surface Evolution Equations

A Level Set Approach

Complex Geometry and Mathematical Physics

Complex Analysis Versus General Relativity Theory (Book III-C)

Collected Papers of Y. Matsushima

SERIES IN PURE MATHEMATICS

Differential Geometric Methods in Theoretical Physics : Twentieth International Conference

Twentieth International Conference

Differential Geometry : Proceedings of the Symposium in Honor of Professor Buchin Su's 90th Birthday

Proceedings of the Symposium in Honor of Professor Buchin Su's 90th Birthday

Differential Geometry and Topology

Gauge Gravitation Theory

Geometry in Partial Differential Equations

Geometry and Topology of Submanifolds VI

Harmonic Maps

Concise Complex Analysis

Selected Papers of Wilhelm P. A. Klingenberg

SERIES IN PURE MATHEMATICS

This product is categorised by