01- Read the Nature - Lire la nature - 01
1 Patterns in nature
Why does a soap bubble floating in the air like a perfect sphere ?
Why does nature create regular structures and predictable movements as gravity ?
Mathematicians and physicists use simple models: circles and spheres, squares and cubes, helix, conics…
However, the telescope and the microscope reveal that from the infinitely large to the infinitely small, nature has more complex forms: spirals, fractals…
Mathematics: Numbers, differential equations, allow us to have a better understanding of life on the Earth or the structure of the Universe.
2 Is the world fractal ?
How can we represent the shape of a winding river, a rugged coastline ?
The shape of a cloud, a flame or a weld?
Can we determine the dimensions of galaxies in the Universe ?
Can we model the intricate branching of activitie on the world wide web ?
Observe a fern leaf. It is built by repeating of the same motif on ever decreasing scales.
Such structure which often appears in nature led Benoit Mandelbrot to develop Fractal geometry.
A fractal is a self-similar shape every part of which looks like a smaller version of the whole. • Mandelbrot (born in 1924, Poland)
3 All in orbit !
How can we describe the orbits of planets, natural or artificial satellites ?
Kepler showed that these orbits are conics - ellipses, parabolas, hyperbolas.
Comets that reappear periodically also have elliptic orbits.
A satellite can free itself from the pull of the solar system by leaving its elliptic orbit to take place on an hyperbolic trajectory.
To follow and to direct the movements of the many artificial satellites circling the Earth, we use rosaries of… parabolic antennas.