TWO mathematicians from Dublin's Trinity College have found a new solution to the age-old conundrum of how to pack a given space without wasting it. They have designed an object that has broken a 107-year-old record for the most efficient filler of 3-dimensional space.
The problem of finding identical objects, all of them constructed of the least amount of material but occupying the largest space, has intrigued scientists for a long time. Although cubes can be packed together without leaving any gaps, they have a large surface area and would require a lot more material than, say, spheres. But when spheres are stacked layer by layer, they leave yawning chasms between them.
It became evident long ago that a compromise between sphere and cube could yield a solution to the problem. Over 100 years ago, Lord Kelvin had designed a 14-sided figure -- sculpted by slicing off six vertices of an octahedron, a solid figure with eight triangular faces, all slightly curved faces to minimise surface area -- that was the most efficient filler of space yet.
Now, in February's issue of Philosophical Magazine, D Weaire and R Phelan claim to have recently designed an object that leaves 0.3 per cent less space than Kelvin's objects when packed together into a given space. The new object consists of eight polyhedra of equal volumes, of which six are 12-sided and two are 14-sided.
Weaire and Phelan took the structure of dry foam as the basic unit to generate an array of 14-sided cells of unequal sizes. Using computer software, the faces and edges of the polyhedra were gently curved to make them all of equal size. Thus Weaire and Phelan were able to design a new structure that busted (although by a subtly minuscule margin of 0.3 per cent) Kelvin's long-standing record.
Stephen Hales, a distinguished biologist from Newton's era, showed some mathematical ingenuity when he tried squashing as many peas as he could into a barrel. The peas were found crushed into deformed shapes with 13 to 14 sides. But since using peas as packing material is a messy exercise, Kelvin had to look to crystal lattices to find a solution.
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