The Pursuit of Perfect Packing, Second Edition

Prefaces

How Many Sweets in the Jar?

Loose Change and Tight Packing

A Teasing but Tractable Problem

A Handful of Coins

Order and Disorder

Hard Problems with Hard Spheres

The Greengrocer’s Dilemma

Ordered Close Packing—The Kepler Problem

The Kepler Conjecture

Marvelous Clarity, Neurotic Anxiety: The Life of Kepler

Progress by Leaps and Bounds?

Proof Positive?

News from the Western Front

The Programme of Thomas Hales

At Last?

Polishing Off the Programme

The Acceptance of Proof

The Flyspeck Project

Who Cares?

The Power of Thought

Disordered Packings

Balls in Bags

A New Way of Looking

How Many Balls in the Bag?

Is the Bernal Close Packing Well Defined?

Bernal’s Long-Running Ball Game

Tomography Takes Over

Sands and Grains

Granular Materials

Osborne Reynolds: A Footprint in the Sand

Major Bagnold’s Desert Drive

Dunes

Order from Shaking

Segregation

Granular Temperature

Divide and Conquer: Tiling Space

Packing and Tiling

The Voronoï Construction

The Dual Construction of Delaunay

Applications

Vertices in Tilings

Three Dimensions

Regular and Semiregular Packings

Peas and Pips

Vegetable Staticks

Stephen Hales

Pomegranate Pips

Biological Cells, Lead Shot, Rubber Balls, and Soap Bubbles: Plus ça Change

Enthusiastic Admiration: The Honeycomb

The Honeycomb Problem

What the Bees Do Not Know

A Search for Structure

A Voice in the Wilderness

The Two-Dimensional Soap Froth

The Rules of the Game

In a Cambridge Garden

Toils and Troubles with Bubbles

Playing with Bubbles

A Blind Man in the Kingdom of the Sighted

Proving Plateau

Foam and Ether

The Kelvin Cell

Most Beautiful and Regular

The Twinkling of an Eye

Simulated Soap

A Discovery in Dublin

Crystals of Small Bubbles

Bubbles in Beijing

An Olympian Vision

Fun and Fit for Purpose?

A Flexible Friend?

The Architecture of the World of Atoms

Molecular Tactics

Atoms and Molecules: Begging the Question

Atoms as Points

Playing Hardball

Modern Crystallography

Crystalline Packings

Packing Tetrahedra

Changed Utterly: Quasicrystals

Amorphous Solids

Crystal Nonsense

Apollonius and Concrete

Mixing Concrete

Apollonian Packing

Packing Fraction and Fractal Dimension

Packing Fraction in Granular Aggregates

Packings and Kisses in High Dimensions

Packing in Many Dimensions

A Kissing Competition

Kissing the Neighbors in Higher Dimensions

Will Disorder Win in the End?

The Sweets in the Jar, the Pebbles on the Beach

Those Sweets

Hey, What Shape Do You Want Your Ice Cubes?

Another Walk on the Beach

The Giant’s Causeway

Worth Seeing?

Idealization Oversteps Again

The First Official Report

Mallett’s Model

A Modern View

The Last Word?

Lost City?

Finite Packings and Tessellations, from Soccer to Sausages

The Challenge of a Finite Suitcase

Soccer Balls

Golf Balls

Buckyballs

Buckminster Fuller

Graphenes

The Thomson Problem

Packing Points on a Disk

The Tammes Problem

Universal Optimal Configurations

Helical Packings

Virus Architecture

Stuffing Sausages

Filling Boxes

The Malfatti Problem

Odds and Ends

Ordered Loose Packings

Parking Cars

Goldberg Variations

Packing Regular Pentagons

Dodecahedral Packing and Curved Spaces

Microspheres and Opals

Protein Folding

The Tetra Pak Story

Packing Regular Tetrahedra

Nature and Geometry

Appendix A: The Best Packing in Two Dimensions

Appendix B: Turning Down the Heat: Simulated Annealing

Index