mathematics

The Pursuit of Perfect Packing

The Pursuit of Perfect Packing is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand The Pursuit of Perfect Packing rather than just read about it. In short: The Pursuit of Perfect Packing is a book on packing problems in geometry. It was written by physicists Tomaso Aste and Denis Weaire and published in 2000 by Institute of Physics Publishing (doi:10.1887/0750306483, ISBN 0-7503-0648-3) with a second edition published in 2008 by Taylor & Francis (ISBN 978-1-4200-6817-7).

Key takeaways

The Pursuit of Perfect Packing belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect The Pursuit of Perfect Packing to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of The Pursuit of Perfect Packing from memory before moving on to harder problems.

Reference excerpt

The Pursuit of Perfect Packing is a book on packing problems in geometry. It was written by physicists Tomaso Aste and Denis Weaire and published in 2000 by Institute of Physics Publishing (doi:10.1887/0750306483, ISBN 0-7503-0648-3) with a second edition published in 2008 by Taylor & Francis (ISBN 978-1-4200-6817-7).

Topics The mathematical topics described in the book include sphere packing (including the Tammes problem, the Kepler conjecture, and higher-dimensional sphere packing), the Honeycomb conjecture and the Weaire–Phelan structure, Voronoi diagrams and Delaunay triangulations, Apollonian gaskets, random sequential adsorption, and the physical realizations of some of these structures by sand, soap bubbles, the seeds of plants, and columnar basalt. 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, Joseph Plateau, Lord Kelvin, Osborne Reynolds, 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

Worked examples

Example 1 — a first encounter with The Pursuit of Perfect Packing

Start with the simplest possible case. Write down what The Pursuit of Perfect Packing claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to The Pursuit of Perfect Packing before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about The Pursuit of Perfect Packing ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of The Pursuit of Perfect Packing

In research: The Pursuit of Perfect Packing appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses The Pursuit of Perfect Packing in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: The Pursuit of Perfect Packing is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2000 non-fiction books, 2008 non-fiction books, Packing problems, so understanding it makes those chapters shorter.
In everyday life: Look for The Pursuit of Perfect Packing outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study The Pursuit of Perfect Packing in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what The Pursuit of Perfect Packing means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain The Pursuit of Perfect Packing out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is The Pursuit of Perfect Packing in simple terms?

Why does The Pursuit of Perfect Packing matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study The Pursuit of Perfect Packing?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on The Pursuit of Perfect Packing.