Maths and art
Intersections between mathematics and artistic expressions: music, painting, architecture, design
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.
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.
Pierre-Simon Laplace: a giant for the ages | Tangente
Laplace's scientific output is colossal. A tireless researcher, the "French Newton" also devoted himself to making the latest discoveries widely known and to providing scientific training for new generations.
Laplace, unloved by historians: an ambiguous portrait | Tangente
Although Laplace's scientific work is recognized worldwide, his political role remains controversial and is sometimes disparaged. Historians often judge him harshly—when they do not ignore the scientist altogether. Does this reflect a French difficulty in finding a place for science in the shared cultural imagination?
From rhomb to rhombus
For many people, the rhombus—originally called a "rhomb" (see In Brief, "The origin of the rhombus"; the associated adjective is still "rhombic")—is characterized by its acute angles pointing upward and downward. Yet, as Euclid already observed, this quadrilateral is defined by the equal lengths of its sides. Its ability to form tilings accounts for its use in architecture and decoration.
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…
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.
Dust in the corners
The beauty of fractal curves fascinates amateurs and seasoned mathematicians alike. The latter, however, know that these objects also give rise to subtle problems in measure theory. Here we illustrate an apparently paradoxical situation and a delicate theorem.
Portrait of Luca Pacioli: A mathematical brief | Tangente
Until January 8, 2024, the Louvre Museum is hosting an exhibition that should interest all our readers: "Naples in Paris: The Louvre Hosts the Museo di Capodimonte."
Galois manuscript mystery solved | Tangente
A contributor to the les-mathematiques.net forum, known by the username anqian, recently solved a small mystery that successive editors of Galois's works had puzzled over in vain.
Adolphe Quetelet and the average man in statistics | Tangente
Born in Ghent on February 22, 1796, French, then Dutch, and finally Belgian after 1830, Adolphe Quetelet (1796–1874) was the very model of a cultured polymath. After defending a thesis in geometry, he worked in scientific fields beyond pure mathematics.
Artists’ visions: knots in art and maths | Tangente
Three artists share their visions of knots.
Stereographic projection
Since 2021, the Bourse de commerce in Paris has been open to the public, showcasing contemporary art from the Pinault Collection. Its superbly renovated interior offers mathematicians an opportunity to explore… stereographic projections!
Art and the sphere: when mathematics inspires | Tangente
A brief look at several artists who have made the sphere their subject.
Aperiodic tiling: the ein stein tile | Tangente
Some craftspeople have become masters of the art of tiling, such as those who were commissioned to decorate the Alhambra palace in Granada, Spain. This inevitably raises geometric questions. Which tiles can cover the plane? What symmetries emerge?
Writing a treatise on sound at the age of 11 | Tangente
The links between music and mathematics are well established. There was a time when it was not unusual for the most learned minds to pursue both with equal delight. Pascal, too, is said to have explored questions relating to sound, further evidence of his astonishing precocity.
A master of mathematical induction
Mathematical induction is a major tool in mathematical proofs. On at least three occasions, Pascal explicitly uses reasoning that is "almost" mathematical induction, making him one of the method's inventors.
Tangente turns 35
December 4, 2022: a milestone for Tangente, which celebrated its 35th anniversary at the Musée des arts et métiers in Paris. 2,050 visitors enthusiastically took in the shows, talks, workshops, exhibitions, meet-and-greets, presentations, ceremonies and more on offer. Here is a glimpse of that memorable day.
Geometric puzzles at infinity
Some of the most famous sangaku figures echo other mathematical constructions, forging beautiful connections between results established in different places and at different times. Here is a particularly striking example.
Curves made of straight lines: string art | Tangente
String pictures—decorative designs drawn or made with thread or cord—enjoyed their heyday around 1975. Today they are back in fashion under the name string art.