''The Pursuit of Perfect Packing'' is a book on

packing problems Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few conta ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

. It was written by physicists Tomaso Aste and

Denis Weaire Denis Lawrence Weaire FRS (born 17 October 1942 in Dalhousie, Simla, India) is an Irish physicist and an emeritus professor of Trinity College Dublin (TCD). Educated at the Belfast Royal Academy and Clare College, Cambridge, he held positions a ...

, and published in 2000 by Institute of Physics Publishing ( doi:10.1887/0750306483, ) with a second edition published in 2008 by Taylor & Francis ().

Topics

The mathematical topics described in the book include

sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...

(including the

Tammes problem In geometry, the Tammes problem is a problem in packing a given number of circles on the surface of a sphere such that the minimum distance between circles is maximized. It is named after the Dutch botanist Pieter Merkus Lambertus Tammes (the n ...

, the

Kepler conjecture The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling s ...

, and higher-dimensional sphere packing), the

Honeycomb conjecture The honeycomb conjecture states that a regular hexagonal grid or honeycomb has the least total perimeter of any subdivision of the plane into regions of equal area. The conjecture was proven in 1999 by mathematician Thomas C. Hales. Theorem Le ...

and the

Weaire–Phelan structure In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution ...

Voronoi diagram In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed ...

s and

Delaunay triangulation In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle o ...

Apollonian gasket In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three. It is named after Greek ...

s, random sequential adsorption, and the physical realizations of some of these structures by sand, soap bubbles, the seeds of plants, and

columnar basalt Basalt (; ) is an aphanitic (fine-grained) extrusive igneous rock formed from the rapid cooling of low-viscosity lava rich in magnesium and iron (mafic lava) exposed at or very near the surface of a rocky planet or moon. More than 90% o ...

. A broader theme involves the contrast between locally ordered and locally disordered structures, and the interplay between local and global considerations in optimal packings. As well, the book includes biographical sketches of some of the contributors to this field, and histories of their work in this area, including Johannes Kepler,

Stephen Hales Stephen Hales (17 September 16774 January 1761) was an English clergyman who made major contributions to a range of scientific fields including botany, pneumatic chemistry and physiology. He was the first person to measure blood pressure. He al ...

, Joseph Plateau,

Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did important ...

Osborne Reynolds Osborne Reynolds (23 August 1842 – 21 February 1912) was an Irish-born innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. ...

, and J. D. Bernal.

Audience and reception

The book is aimed at a general audience rather than to professional mathematicians. Therefore, it avoids mathematical proofs and is otherwise not very technical. However, it contains pointers to the mathematical literature where readers more expert in these topics can find more detail. Avoiding proof may have been a necessary decision as some proofs in this area defy summarization: the proof by Thomas Hales of the Kepler conjecture on optimal sphere packing in three dimensions, announced shortly before the publication of the book and one of its central topics, is hundreds of pages long. Reviewer Johann Linhart complains that (in the first edition) some figures are inaccurately drawn. And although finding the book "entertaining and easy to read", William Satzer finds it "frustrating" in the lack of detail in its stories. Nevertheless, Linhart and reviewer Stephen Blundell highly recommend the book, and reviewer Charles Radin calls it "a treasure trove of intriguing examples" and "a real gem". And despite complaining about a format that mixes footnote markers into mathematical formulas, and the illegibility of some figures, Michael Fox recommends it to "any mathematics or science library".

References

{{DEFAULTSORT:Pursuit of Perfect Packing, The Packing problems Mathematics books 2000 non-fiction books 2008 non-fiction books