Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
The gravity equation
For once, an economist is talking about an "equation"—which makes it worth a closer look
Gérard Tronel: A life devoted to mathematics | Tangente
Mathematician Gérard Tronel, a great friend of the Tangente editorial team, had been battling cancer for years. He passed away on August 25.
Maryam Mirzakhani: a star has just gone out | Tangente
The brilliant Iranian mathematician Maryam Mirzakhani died of breast cancer on 15 July 2017, at the age of 40
On inscribed angles
The inscribed angle theorem is one of the key results of elementary Euclidean geometry. It requires few tools to state—or even to prove—and has many consequences.
And the angle makes history…
The so-called inscribed angle theorem, still part of every middle-school student's mathematical toolkit today, was already known to ancient geometers. It can sometimes have unusual applications.
2018 Championship
The 32nd Mathematical and Logical Games Championship, organized by the Fédération française des jeux mathématiques, is under way. Tangente brings you an exclusive look at the eighteen problems from the individual quarterfinals.
Tangente turns 30
A grand celebration awaits you on Sunday, December 3, at the Musée des arts et métiers in Paris to mark Tangente's 30th anniversary, followed by an event in Brussels on December 8 and 9. No one is left out: there will be something for everyone, whatever their age or level.
Special effects
Computer-generated imagery (sometimes called "3D") makes it possible to create fictional worlds on a computer, whether ultra-realistic or cartoon-like, according to the wishes of graphic designers, filmmakers and artists… But how do you create a world? With mathematics!
Fractals in film: from geometry to special effects
Fractal geometry was central to the earliest computer-generated imagery on the big screen. The study of self-similar forms found in nature gave rise to the first computer-generated images… and thus spawned an entire entertainment industry!
Georges Méliès: special effects, anamorphosis and maths
Georges Méliès is often described as the creator of cinematic spectacle, while the Lumière brothers are the inventors of the cinematograph. In fact, Méliès was passionate about technology. He found solutions to problems that can readily be expressed in mathematical terms.
Three camera forerunners: from Marey to the Cinematograph
The pioneers of cinematography used objects that were sometimes unusual, which you can still admire at the Musée des arts et métiers (60 rue Réaumur, 75003 Paris).
Mathematics in fiction films
The world of mathematics is sometimes represented on screen, with varying degrees of success. Films offer a jumble of simple plot devices, biopics, realistic or imagined depictions of the mathematical world, and even the scientific fiction theorized by Denis Guedj.
Dissections: Greg Frederickson's trilogy | Tangente
Greg Frederickson's trilogy is regarded as THE definitive reference on geometric dissections.
The seven types of frieze | Tangente
A tiling covers the plane, extending infinitely in two dimensions; a frieze extends in just one direction. The quintessential decorative motif, it is the decorative border you can put above your wallpaper. There can be only seven different types.
The mosaics of the Alhambra in Granada
The decorative patterns of the Alhambra in Granada, a fortress built in the 14th century, encompass all the symmetry groups of plane tilings that can be repeated using two nonparallel translations. But this finding is recent, incomplete and somewhat controversial...
Seventeen groups that tile the plane
The plane tiling theorem states that the weight of a motif must equal 2. This small value makes it possible to consider every possible wallpaper symmetry: there are only seventeen wallpaper groups.
Dissecting an obtuse triangle | Tangente
The problem of dissecting an obtuse triangle was proposed by Martin Gardner in Scientific American.
Rep-tiles | Tangente
The self-similarity requirement has led to many interesting results on tilings
Puzzles: useful resources | Tangente
Signature and the tiling theorem | Tangente
Have you ever noticed? In friezes, tilings and other periodic patterns that repeat or exhibit symmetries, the artist's range of possibilities is actually quite limited. A fundamental theorem provides a complete enumeration of these patterns.