08 - Optimisation - Optimiser - 08

1 Nature is economical

A soap bubble is spherical; stellar bodies are almost spherical. Why?
At a constant area, a circle defines the surface with the smallest perimeter.
At a constant volume, the sphere has the smallest surface.
Nature takes the easy way.
A liquid mass in relative equilibrium, a drop of oil in suspension or rotating in a liquid, planets when they are being formed, take on spherical shapes, either unique or multiple.

These shapes have the least potential energy which is proportional to their body surfaces.

2 The Earth under
surveillance

How does one find a good representation of the earth? That depends on the use one wishes to make of it.
After having found cartographic projections adapted, for example, to navigation, today we seek to exploit images taken by satellites or from the air to optimize surveillance or the management of resources.
For each pixel of an image one determines the type of terrain - rock, sea, river, forest, the type of cultivation ...
By combining the information supplied by measuring instruments (high resolution spatial and spectral sensors) learning algorithms can be developed.

The models thus constructed are validated by observations on the ground.

3 The most efficient shapes

Why is the honeycomb structure of a bee's nest used more and more? Have bees found the optimal solution?
Materials designed using the honeycomb structure have the advantageous properties of being lightweight, strong and rigid. Honeycomb materials made in aluminium are used in the building of the Airbus A380, the TGV, satellite walls...
Paper or polyvinyl honeycomb materials are currently used for doors and pallets.

The cell of a honeycomb is not, however, the most efficient shape to occupy a given volume. A better way has since been found, but the best shape is still not known.

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