A burning issue for fatties like me is whether you can make a low-fat Black Forest gateau. The answer, surprisingly, can be found in two new science books. The Pursuit of Perfect Packing by Tomaso Aste and Denis Weaire tells you how to pack the cherries in the middle of the cake as densely as possible so that the absolute minimum of cream is required. Universal Foam by Sidney Perkowitz gives insights into how to incorporate vast amounts of air when whipping the cream into a stiff foam.

The question of just how closely you can pack identical spheres has been around for many years. I was fascinated to read in Aste and Weaire’s book that in 1591 Walter Raleigh commissioned some military research to find a formula for the number of cannon balls in a stack. The problem was easy enough for Thomas Harriot to solve without much difficulty, but may well have been the beginning of the search to find the closest possible packing.

Not long after this, Johannes Kepler was amongst the first to state that hexagonal close packing gave the highest possible density. But despite the fact that all physicists “knew” and all mathematicians “believed” that there could not be any denser arrangements of spheres, the formal proof remained elusive. Indeed, the proof put forward by the American mathematician Thomas Hales in 1998, while generally accepted, is still being tested for any possible errors or omissions.

The Pursuit of Perfect Packing not only describes the mathematics surrounding the various ways that spheres and other shapes may be packed together, but also brings a real sense of humour and fun to what might otherwise seem a dry theoretical topic. The brief biographical sketches of some of the important players bring them to life. I treasure the image of J D Bernal being chased down a street by an irate naval officer carrying a revolver after “a brusque interruption of an amorous interlude”. And the description of Kepler as a “nerd” is justified by the fact that he “carefully analysed the merits of no less than 11 girls – before choosing the wrong one [to be his wife])”.

More recent developments are animated with reproductions of e-mail correspondence announcing breakthroughs and discussing results. Some knowledge of the language of maths and physics is useful when reading Aste and Weaire’s book, as they do not shy from inserting equations or using mathematical terminology. Indeed, I find it odd that they should criticize crystallographers for mystifying many with the definition of a crystal as “any solid with an essentially discrete diffraction diagram” (in an attempt to include the recently discovered aperiodic crystals), while seeing nothing strange in writing that “the sausage conjecture states that for d greater than or equal to 5 the arrangement of hyperspheres with a minimal volume convex hull is always a ‘sausage’ “. But despite occasional complexities such as these, this is a very readable and enjoyable book that I would recommend to any student learning crystallography. It certainly contains one of the clearest descriptions of aperiodic crystals I have seen to date.

Universal Foam covers some of the same ground as The Pursuit of Perfect Packing. Both books look at the internal structure of a foam: the shapes of the bubbles. Both begin with Joseph Antoine Ferdinand Plateau, the blind scientist who was the first to work out the three simple rules governing the internal structure of foam bubbles. They relate the story of how Kelvin deduced that the shape should be a tetrakaidecahedron and how he made a wire model of his idealized foam known as “Kelvin’s bedspring”. Both also go on to show that this is an unrealistic model, before describing our current best model of “Weaire-Phelan” cells, which can be observed in real foams.

It is perhaps not surprising that Weaire and Aste provide the clearer narrative of later developments in this area as they are active researchers in the field. All the different shapes are well illustrated in their book, together with a photograph of Kelvin’s “bedspring”, although the latter is expressed only in words in Perkowitz’s book. To me, though, it is a little disappointing that the clearer explanation is found in the more academic text and not in Perkowitz’s supposedly “popular-science” book.

But it would be unfair to suggest that Universal Foam is not a good popular-science book. It takes the reader on an imaginative trip through the science and uses of foams. Along the way, Perkowitz shows that foams are ubiquitous. He defines a foam as any substance with lots of small voids inside. This takes us well beyond our normal expectations of foams as collections of soap-like bubbles and into a variety of fascinating materials, such as the ultra-light and strong aerogels, as well as systems as diverse as cork and living cells.

Each chapter is devoted to a particular type of foam and consists of several short essays about different aspects of that foam. So, for example, in the chapter on living foam we learn about cell division; about bone and lung structure; how fish and frogs use foams to help aerate and protect their eggs; and even about “mad-cow” disease.

With such a wide range of topics the book is sometimes repetitive as the author tries to ensure that each section is self-contained and can be read without the need to read the whole book. This style makes Universal Foam an ideal book to dip into and discover yet another interesting new aspect of foam.

So can these books really help reduce the fat in a Black Forest gateau? If one assumes that normally one just whips the cream until it is stiff enough to hold its own weight and that the cherries are randomly packed in the middle of the cake, then significant reductions could be made. Carefully packing the cherries (and deforming them into polyhedra) can reduce the space to be filled by the cream by at least a factor of two, while adding surfactants (such as egg white) to the cream while whipping can increase the volume of air incorporated by another factor of two. In other words, the fat content might go down by a factor of four or more.

These two books are not only good to read. They can also be good for your health!