All articles
Dive into the fascinating world of mathematics with our captivating articles, written by passionate experts. Whether you are a curious amateur or a seasoned mathematician, our articles cover a wide range of topics, from fundamental concepts to the latest discoveries, including practical applications and philosophical reflections.
The slow emergence of Euclidean spaces
The axiomatic definition of the dot product provided a rigorous and fruitful framework for studying metric properties—those involving distance, angle, and orthogonality. This concept did not emerge clearly until the 1920s.
Translations and rotations – Maths brief | Tangente
Translations and rotations have many applications—and not only in geometry!
First examples of vector spaces (2)
Every good vector space E needs a base field K. But what exactly is a field?
The determinant: an essential tool in linear algebra | Tangente
The determinant provides a criterion for determining whether an endomorphism is bijective. Its geometric interpretation also tells us about the nature of linear transformations.
Latin, a source of new words – maths brief | Tangente
The development of linear algebra gave rise to new terms, such as "scalar", and revived others, such as "vector".
First examples of vector spaces (1)
Before we get to the heart of the matter, it is worth remembering that we have all encountered a vector space at school.
A revolutionary concept!
From the geometric motivations of the earliest scholars to its axiomatization around 1900, the concept of a vector space was gradually refined into the indispensable foundation of many mathematical theories. Here is its thrilling story.
Gaston Darboux: geometer and artist
Gaston Darboux, whom we commemorate this year, died a century ago. Throughout his life, he remained "a young man of the rarest learning and the highest promise," and he left behind a considerable body of work. His geometric results on orthogonal surfaces are spectacular.
A remarkable story: 30 years of making mathematics accessible
Who would have wagered in 1987, when a handful of enthusiasts had the outlandish idea of creating a professionally produced magazine devoted to the place of mathematics in the world, that Tangente would still be going thirty years later—and would become the leading reference for mathematical culture?
Cryptographic machines: a history of encryption
Since antiquity, people have sought to ensure the secrecy of their correspondence through encryption. Because simple methods were easily decrypted, more sophisticated ones were invented, but they were difficult to use by hand. Machines therefore became essential.
The fascination of gears: geometry and mechanics
Gears are both objects of fascination and symbols of mechanics. Determining the shape of their teeth is a sophisticated mathematical problem. Yet this long history, which stretches back to antiquity and is still being written, remains remarkably little known!
2017 Tangente Awards: the winners
The Tangente Awards are becoming an increasingly well-known fixture in publishing and education. A look back at the 2017 awards, which were just presented on December 4 at the Palais du Luxembourg.
A tour of the Museum of Machines: mathematics and mechanisms at the CNAM
Mathematics isn't visual? You can't really represent it "in the real world," let alone make it tangible? Think again! The Musée des arts et métiers (60 rue Réaumur, 75003 Paris) invites you to revisit its collections… through the surprising lens of mathematics.
Ulysse Lacoste: art, mathematics and performance
Mathematics, art, poetry, craftsmanship, kinematics, performance… Ulysse Lacoste's work embraces all this and more, blurring boundaries in pursuit of a distinctive alchemy that sets this singular artist's approach apart.
Two magnificent reissues: Fenouillard, Camember, Cosinus
Two recent—and entirely different—initiatives deserve attention.
An interactive journey through mathematical history
Reading Tangente already lets us travel through mathematical time and space—but have you ever thought of taking a virtual tour around the world and, at each stop, discovering the full history of mathematics rooted there?
Best illusion of 2017: Dynamic Müller-Lyer
The 2017 edition of the Best Illusion of the Year Contest, an annual international optical-illusion competition, took place in early October.
Publimath turns 20: the mathematics database
Publimath is a treasure trove of bibliographic resources for mathematics enthusiasts and educators alike.
Spiral Jetty: Great Salt Lake's mathematical spiral
In 1970, American land-art pioneer Robert Smithson used bulldozers to create an enormous spiral of volcanic rock northeast of the Great Salt Lake, in Utah, in the western United States
Bull's-eye: the results
Tangente's 30th anniversary coincides with another milestone: the 20th anniversary of Affaire de Logique, the weekly column in Le Monde, which celebrated its 1,000th installment with a competition run weekly for 26 weeks that drew… 1,000 participants!