All maps are wrong!
Submitted by Michel Darche on
C. F. Gauss (1777-1855) showed that it is impossible to preserve all ratios of distances when drawing a planar map of a region of the Earth. But do we need to sacrifice everything?
Exhibitions
Where is the sun at noon?
Submitted by Michel Darche on
Have you already remarked that the middle of the day (or solar noon) is not always at the same time on your watch? The sunset is sooner on December 10 than at the winter solstice. If you observe the Sun at noon every day, then its position draws a figure eight curve, called analemma, with endpoints at the winter and summer solstices.
Tectonic Plates
Submitted by Michel Darche on
From the inner core to the surface the Earth temperature decreases. This induces convection movements in the Earth’s mantle. The warmer magma moves closer to the surface where it cools down. It then sinks inside the mantle and a new cycle is started. This induces movements of the rigid tectonic plates at the surface, and shears.
Satellites under control
Submitted by Michel Darche on
Telecommunications, navigation, meterorology, etc., but also cell phones, GPS, Internet, provide numerous reasons to install satellites orbiting around the Earth. For this purpose, mathematicians select and optimise trajectories and orbits of spacecrafts with more and sophisticated techniques.
Permeable or impermeable?
Submitted by Michel Darche on
The study of the diffusion of liquids in the soil, also called percolation, allows scientists measuring how water is diffused in the soil, how fast aquifers refill, and to understanding the diffusion of gas, petrol and pollutants in the soil.
It is the English mathematician J. M. Hammersley who, in 1965, highlighted that diffusion and percolation also occur in telecommunication networks, the spreading of epidemics, propagation of fires, and the phase transition from water to ice.
Braids
Submitted by Ester Dalvit on
A journey through the mathematical theory of braids.
CHAOS
Submitted by Jos Leys on
A two hour film on dynamical systems: see www.chaos-math.org
Coriolis force
Submitted by Michel Darche on
Have you already tried to reach a target when you are moving to the right? You need to aim at the left of the target if you wish to reach it. Same thing if the target is moving slower than you. Your target seems to be deviated by a fictitious force, the Coriolis force. It is the French mathematician G. G. de Coriolis (1792-1843) who was the first to explain the influence of the Earth rotation on the winds and marine streams. He did so through theoretical work on composed centrifugal forces.
Solitons and Tsunamis
Submitted by Michel Darche on
Solitons are solitary waves observed for the first time by the Scottish mathematician and engineer J. S. Russell in 1834. Solitons travel very long distances at a constant speed without loss of energy. Their speed is proportional to the square root of the deepness of the channel.
Where are you?
Submitted by Michel Darche on
How many satellites orbiting around the Earth are needed to compute exactly one’s position at each instant?
The GPS system uses a set of satellites (at least 24) orbiting around the Earth and emitting signals.
An ideal GPS receiver measures the travel time of three signals from emitted by three satellites to the receiver. From each measure it computes its distance to each satellite.