Curiosity
Patterns, crafts, magic squares and fun mathematical content not part of the school curriculum
Coming to grips with decimal expansions
Like any real number—for example, pi—a fraction can be written as a finite or infinite decimal expansion. Remarkably, the resulting decimal expansion is always eventually periodic.
Gears
How can a ratio be approximated by a simpler one? Crucial to clockmakers and engineers, this problem can be solved with a healthy dose of arithmetic and algorithms dating back to antiquity.
Calculating? With calculi, of course! | Tangente
It is hard to believe that the multiplication and division methods we learn at school did not become universally adopted in the West until the 18th century. So how did people calculate before then? They used calculation aids such as counting boards.
Multiplying with rods | Tangente
Before the advent of modern technology, techniques or tools had to be devised to perform the basic calculations required by craftspeople, engineers and everyone else! From John Napier to Édouard Lucas, mathematicians distinguished themselves in this pursuit.
The centenary of Gustave Eiffel's death
Gilles and the mathematics culture and games fair | Tangente
Two passions guided Gilles throughout his life: puzzles and popularizing mathematics.
The culture of Tangente | Tangente
From the outset, Tangente envisioned a whole world of worlds: mathematics linked to literature and poetry, to music; a publication opening the door to the wonderful world of logical puzzles; mathematics as a whole world in itself, extraordinarily vibrant and fully in tune with the latest technological advances. Above all, it stood for openness to the world, through writing that aimed to be accessible to everyone.
2024: a new year with many properties
What spectacular mathematical advances, major scientific discoveries and gains in knowledge does the new year have in store for us? It is hard to say! What is certain is that the natural number 2024 abounds in wonderful arithmetic and combinatorial properties…
The "A Matter of Logic" column | Tangente
"A Matter of Logic" is a weekly column in the newspaper Le Monde, written since 1997 by Gilles Cohen and Élisabeth Busser. In 2000, it earned them the D’Alembert Prize for popularizing mathematics, awarded by the Société mathématique de France.
A form of harmony between geometry and arithmetic
Many mathematicians have taken an interest in figurate numbers. But their concerns have not always been the same! In ancient times, people sought to construct and represent numbers using counters. The resulting shapes illustrate a host of arithmetic relationships.
Mathematics and literature | Tangente
Gilles Cohen has always championed breaking down the divide between literary and scientific backgrounds. To him, the two are not only perfectly compatible but also mutually enriching.
Francesco Maurolico's extensions
A member of a Greek family that emigrated to Sicily after the fall of Constantinople, Francesco Maurolico was born in Messina in 1494 and died there in 1575. He entered the Church at the age of 27, proposed an extension of figurate numbers, and established many of their arithmetic properties.
An inventory of arithmetic puzzles | Tangente
Figurate numbers, which provide a visual representation of integers, form a wonderful bridge between geometry and arithmetic. Some properties in either field can be reformulated in the other, and vice versa! New questions naturally arise…
A new life for figurate numbers
Figurate numbers entered Arabic mathematics through Thabit ibn Qurra’s translation of the work of the mathematician and philosopher Nicomachus of Gerasa. Thabit’s name is associated with Thebit numbers (the "e" replacing the "a" in medieval Latin transcription).
A life spent sharing mathematics | Tangente
Gilles Cohen was far more than the director of Éditions POLE and its flagship magazine, Tangente. Brimming with projects and ideas, he launched initiatives in every direction to bring mathematics to a wider audience. In recent years, he was chiefly involved in Club Tangente's activities.
2023 Tangente Awards winners | Tangente
Since 2010, the Tangente Club has used the Tangente Awards to honor creative works that showcase mathematics. The winners receive a work of art. The awards ceremony took place at the Musée des Arts et Métiers in Paris on December 3, 2023, during Tangente Day.
On the road – Mathematical brief | Tangente
Both unusual—since it does not usually rest on its "base"—and harmonious, as it is a quadrilateral with four equal sides, the rhombus appeals to graphic artists, advertisers and other designers: it appears in puzzles, games, road signs, logos…
A magic rhombus – mathematics brief | Tangente
In August 2019, our reader Mustapha Rherrad created a magic rhombus using the integers from 1 to 32, arranged so that the sums along every "slanting row" and every "main diagonal" are equal.
La Maison des mathématiques de l’Ouest - Article | Tangente
Activities that bring artists and mathematicians together to share mathematics with the public are flourishing across Pays de la Loire and Brittany. A Maison des mathématiques de l’Ouest was established to bring them together.
The hidden riches of the multiplication table
Think you know your multiplication tables? Think again! A surprising property emerges when a regular polygon is drawn on the multiplication table: the mean of the values at its vertices is the value at the polygon's center!