03 - Filing a Space - Remplir l'espace - 03

1 Piling oranges!

How to pile oranges to occupy the least possible volume?
In displays, oranges occupy 74% of the space. It is the "face-centered cubic packing" which is well known by crystallographers. Kepler thought, four centuries ago, that this arrangement was the best.
It was only in 1998 that it was proved, by studying, with the help of computers, more than 5000 different cases.

This problem of everyday life has applications which include the study of crystalline structures and the theory of codes. But if we want to fill a box of given shape, the problem is still without a general solution.
• Johannes Kepler (1571-1630)

2 From atoms to crystals

Sky, earth, atoms and elementary particles... Why is the sphere (entire or in part) often used to represent natural forms ?
At the microscopic scale, natural phenomena can be modelled by undeformable spheres, moving freely or colliding without loss of energy.

If atoms are modelled as spheres, crystals are thought of as orderly, and most frequently periodic, layers of atoms. These phenomena are like elements of an infinite game of billiards in three dimensions: these models permit the study of gases, liquids and certain solids.

3 Packaging:
a complex problem

Which occupies the smallest volume : a kilo of coffee beans or a kilo of ground coffee ?
This little problem becomes important if you want to transport tons of coffee !

The problem becomes very complex if the items are of different sizes and shapes and are to be transported in well defined containers. Conversely, how should one find the best dimensions for objects to fill a given volume ?

These problems, conditional also on the weight of the objects, the cost of the transport, the expense of storage, etc. have not yet been solved.

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