History and Culture
History of mathematics and cultural connections
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…
Acoustics and computer music: Helmholtz | Tangente
Thanks to the work of Joseph Sauveur and later Hermann von Helmholtz on sound phenomena, we can analyze a sound in terms of its pitch, intensity and timbre. This is the analysis used in computer music, which is so popular with contemporary composers.
Astor Piazzolla and tango nuevo:
The freedom championed by the rise of contemporary music led Astor Piazzolla to break free from the stifling conventions of classical tango, both harmonically and rhythmically, and create a new form. This evolution in musical structure can be analyzed.
A century of mathematical music | Tangente
Since 1945, contemporary "art" music has become so diverse that any overview is now impossible. Yet technology and the introduction of some form of chance or randomness into composition remain ubiquitous.
An invariant under central projection
The need to model visual perception gave rise to a new geometry. Renaissance painters felt compelled to study it closely in order to depict depth. Lengths, angles: nothing seemed to be preserved, apart from a curious relation linking four collinear points…
Pick up your pens: maths writing competition | Tangente
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.
First black hole photograph: Katie Bouman | Tangente
The first photograph of a black hole was produced using an algorithm tasked with assembling all the data collected by a network of telescopes.
Karen Uhlenbeck: first woman to win Abel Prize | Tangente
Following Ingrid Daubechies and Claire Voisin, another female mathematician has been honored this year.
Coloring planar tilings: four colors | Tangente
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.
Intellectual self-defense: zetetics courses | Tangente
Cortecs (Collective for Transdisciplinary Research on Critical Thinking & Science) is a teaching and research collective founded in 2010 to produce educational resources and scientific content, as well as courses and training in critical thinking, intellectual self-defense, zetetics and the scientific method.
High school maths: education's vicious circle | Tangente
On January 24, 2018, the Villani–Torossian report, "21 Measures for the Teaching of Mathematics," was published, generating enthusiasm among the teaching community. That enthusiasm was tempered on February 12 by the announcement of the forthcoming high school reform.
François Viète and algebraic zetetics | Tangente
Henri Broch revived the word "zetetics." Long before him, François Viète (1540–1603) had already used it in a slightly different sense.
Theorizing conspiracy theory through mathematics | Tangente
We often encounter the outlandish claims made by conspiracy-theory enthusiasts. But can we use theory itself to show just how implausible they are?
Russell's teapot and the burden of proof | Tangente
We often hear the phrase "absence of evidence is not evidence of absence." This statement is ambiguous: many fanciful claims cannot be disproved.
Séphora-Berrebi scholarships: 2019 winners | Tangente
The four Séphora-Berrebi scholarships, each worth €2,000, are awarded to female doctoral or postdoctoral researchers who have distinguished themselves through their research in mathematics or computer science.
Maths Night 2019 in Tours and Blois | Tangente
For its fifth edition, the Maths Night festival, held in the Loire Valley, will feature talks, shows, exhibitions and films, all with plenty of humor and conviviality.
Félix, inventor bridging art and mathematics | Tangente
Sculptor, architect, engineer, mathematician? No doubt all of the above! Gérard Chamayou, known as Félix, was one of those who refused to accept barriers between disciplines, and his gift was to move among them with a provocative yet deeply humane spirit.
Three mathematicians honored in 2019 | Tangente
The 2019 L'Oréal-UNESCO For Women in Science Award went to Claire Voisin and Ingrid Daubechies. At the same time, Jean-François Le Gall received the prestigious Wolf Prize.
Knuth's octagons
The American mathematician Donald Knuth created TeX, a mathematical typesetting system based on Bézier curves.
Family reunion
Some geometric figures are a delight to behold: a host of skilfully arranged lines, intertwined with a graceful curve that seems barely to touch each one. What mathematical theory lies behind them? The theory of envelopes of lines.