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The cross-ratio
In modeling visual perception, the Renaissance painters brought forth a new geometry to represent depth. Nothing seemed to be preserved, except a strange relation linking four collinear points, the cross-ratio, which however, since Antiquity, had been glimpsed by Menelaus and Pappus. This invariant, which emerges from the concurrence of four lines, allows geometric constructions and elegant proofs, even in a non-Euclidean setting. It offers a different perspective on the plane, by abolishing the reign of the notions of angle and distance.
Maths and contemporary music
Since Pythagoras, we have known the close links between music and mathematics. In the 20th century, the greatest names such as Boulez, Xenakis or Schaeffer, vied with inventiveness, drawing on probabilities, symmetries and even chaos theory, to create new compositions. Since the advent of synthesizers, the game has been revolutionized and engineers collaborate on musical creations in organizations such as Ircam. Some draw inspiration from rhythms based on simple numerical ratios to revisit popular music such as Argentine tango.
All articles in this issue
A free ticket to the stars?
How far we have come since Newton's famous apple! Recently discovered remarkable properties of the gravitational field raise the prospect of space missions requiring almost no energy—not only to the Moon, but to other planets as well…
Instruments in the service of music
Marking time, giving music its rhythm by keeping the beat: these are the functions of an object that accompanies many musicians—the metronome. Originally mechanical, it later became electronic, no doubt to keep in tune and move with the times…
Jean Bourgain
The prodigious Belgian mathematician Jean Bourgain (1954–2018) worked in many fields of mathematics, forging wholly unexpected links between seemingly separate areas. His outstanding results earned him numerous awards.
Coloring planar tilings
The proof of the four-color theorem caused quite a stir! Results on colorings using only two or three colors have proved less controversial. By considering how to make a beaded necklace, we can take a fresh look at these coloring questions.
Karen Uhlenbeck: the first woman to win the Abel Prize!
Following Ingrid Daubechies and Claire Voisin, another female mathematician has been honored this year.
The first photograph of a black hole, thanks to Katie Bouman
The first photograph of a black hole was produced using an algorithm tasked with assembling all the data collected by a network of telescopes.
Multiplying in quasi-linear time
Multiplying two integers dates back several thousand years. In 2019, at last, the algorithm was improved!
Pens at the ready!
The publication of Daniel Bouix's article "Coloring the Tiles of the Plane" gives us an opportunity to remind readers that the 2019 Best Article Award competition is now under way. Entrants have until September 30 to submit their work.
Arithmetic: Things were better in the old days!
The latest report from the Directorate of Evaluation, Forecasting and Performance warns of declining achievement among pupils at the end of CM2.
Statistical methods in epidemiology
An article in Science et pseudo-sciences explains the statistical methods used in epidemiological studies, using cases of "babies born without arms" as an example