The Kelvin Problem

In 1887, Kelvin posed one of the most discussed scientific questions of the last 100 years - the problem of the division of three-dimensional space into cells of equal volume with minimal area. It has interested mathematicians, physical scientists and biologists ever since and the problem has scientific relevance to foams, emulsions and many other kinds of cells. In the 1990s, a more complex structure was discovered by Robert Phelan and Denis Weaire and it remains the best yet found. This text assesses the various merits of Kelvin's structure and of that discovered by Weaire and Phelan. It also looks at the problem of proof that Weaire's structure having minimal area remains open.