Curiosity
Patterns, crafts, magic squares and fun mathematical content not part of the school curriculum
A history of modular arithmetic
The idea of working with the remainders obtained when numbers are divided by certain integers, rather than with the numbers themselves, gradually gained ground. Gauss formalized the idea with his notion of congruence, giving rise to modern modular arithmetic. Congruences have quite a history!
Poincaré and analytical Cubism: geometry and art | Tangente
As an artistic movement, Cubism grew out of a fundamentally mathematical approach to space, shortly after the publication of La Science et l’Hypothèse. In it, Henri Poincaré discusses the nature of space, and artists would strive to "turn his words into paintings."
Jacques Dominioni, painter of geometry | Tangente
The work of the painter Jacques Dominioni (1934–2014) belongs primarily to lyrical abstraction. Yet his mastery of basic geometric forms—lines, circles and the grid structure underlying his paintings—is thought-provoking... and moving. Let's explore the different periods of his artistic output.
Euclid's algorithm, et cetera
A history of arithmetic—or how an algorithm dating from the third century BCE has endured through the ages and evolved to serve modern disciplines, particularly computer science and cryptology.
Problem-writing competition | Tangente
To mark the publication of issue 200, Tangente organized a problem-writing competition. Nine of the forty-three puzzles submitted received prizes, but many others deserved one too. We asked the jury members to single out their personal favorites.
Creators' secrets
Where do ideas come from when creating a mathematics problem? How can anyone still find original material when so many topics have been explored over the centuries? How do you keep coming up with something new after devising hundreds of problems? How do you entice and engage the reader?
Forerunners in mathematics publishing | Tangente
On a more modest scale, several French-language magazines preceded Tangente. Some of those featured on this page even ceased publication to help launch Tangente.
Magic and curiosities: 7th Math Night | Tangente
For its seventh edition, Math Night will once again be held in Mareau-aux-Prés, a Loire Valley town near Orléans whose mayor, Bertrand Hauchecorne, is none other than the editor-in-chief of Tangente.
A Goncourt for a mathematician | Tangente
Mathematics scored twice in 2021, with two Goncourt Prizes.
Collective decision-making and mathematics | Tangente
Arrow's classic impossibility theorem has often been invoked in political theory to demonstrate the irrationality of democracy. But is this result truly relevant to political science? Let's also revisit some of the mathematical arguments used in the epistemic theory of democracy.
Friendship among numbers | Tangente
In mathematics, being amicable is not the same as having friends...
200, a number like no other!
It can be written as a numeral, 200, or in words, two hundred. Even so, at first glance, the number does not seem particularly interesting. Admittedly, it is not perfect, unlike the eponymous issue of Tangente, but, like Achilles, it is powerful... and therefore fascinating. Here is a brief survey of its arithmetic properties.
Elegant problem-solving methods
The appeal of recreational mathematics is that it requires little formal knowledge. Yet there are ingenious techniques that are hardly ever taught.
Drawing a circle: a geometric challenge | Tangente
During the last lockdown, travel in metropolitan France was restricted to within 10 km of the address where people were staying during that period. Now there is a rule guaranteed to pique the curiosity of mathematics enthusiasts!
The builders' geometric constructions
Several centuries before the Renaissance, whether building a church or a fortress, builders needed only a compass and an unmarked straightedge to draw arcs, pointed arches, basket-handle arches and rose windows. Let us explore the basic geometry behind their methods.
Bernard Cornet's geometric art and Voronoi | Tangente
In art, mathematical tools can help artists develop and create their work. The Nantes painter Bernard Cornet (born in 1952) has brought Voronoi diagrams and Delaunay triangulation into his artistic practice.
Penrose and the Kleenex affair | Tangente
In the 1970s, Roger Penrose filed patent applications for several of his aperiodic tilings (!) and founded a company, Pentaflex, to manage the patent rights.
Homo academicus in his labyrinth | Tangente
Exploring the literary corpus offers an opportunity to highlight some of the logical and paradoxical arguments that can be brought to bear. Let us take a closer look at Le Stratagème (The Stratagem), a story from Jorge Luis Borges's Le Livre de sable (The Book of Sand).
2021 with a twist
As it does every year, Tangente's editorial team brings you a selection of ingenious calculations to celebrate the new year. The locked-down year of 2020 is gone; the year of games has begun. Welcome to 2021!
Dazzling Penrose tilings
Sir Roger Penrose is renowned for his remarkable and foundational work in geometry and cosmology, and for the applications of that work to black holes. It is puzzling, however, that he is famous to the general public for the tiling that bears his name, with its many remarkable properties.