Math for everyone
Mathematical content accessible to everyone
Points on the sphere: the hostile dictators problem | Tangente
How can points be distributed "as well as possible" on a sphere? The idea is to place them "as far apart as possible." With two, three or four points, one might think that the vertices of a regular polyhedron inscribed in the sphere would do the trick. And yet…
Where is the geographic center of France? | Tangente
What do we mean by "the" center of France?
A geometric and historical concept
Etymologically, the word "geometry" means the measurement of the Earth. Geometry has therefore always dealt with "lengths" and "distances." Initially empirical, the concept was gradually refined, structured, and axiomatized from antiquity to the present day—a long journey through both time and space.
Equidistance curves: equidistant points | Tangente
We know how to locate points equidistant from one point, two points, or even two lines—but what about points equidistant from other geometric figures?
Measuring distances in the Age of Enlightenment
In the 18th century, many mathematical treatises dealt with practical geometry. They presented numerous problems involving the measurement of lines, areas and solids, together with their solutions. Various methods were reviewed for measuring the shortest path between two points.
Distances on a sphere: spherical geometry | Tangente
Pioneered by Menelaus of Alexandria in the first century CE, spherical geometry can be a little disconcerting. It is two-dimensional: for example, longitude and latitude are enough to locate any point on the sphere's surface.
The point farthest from France's borders
Where is the "true" center of France? The question sometimes crops up among fans of recreational mathematics and divides enthusiasts of geographical curiosities. Depending on the criterion used to define this center, it may lie in the Cher, the Indre or… the Finistère!
Erdős number: distance between mathematicians | Tangente
Have you heard of the Erdős number, which measures how "close" a researcher is to Hungary's most famous mathematician through successive collaborations?
Berlekamp problem: a strategy game | Tangente
The idea of distance has applications in some unexpected fields. A playful example is the Berlekamp problem, in which Hamming distance makes an appearance—and proves particularly effective!
Interpreting blood test results
In medicine, an atypicality index defined using specific distance measures can determine whether blood test results are considered pathological.
A stroll through the solar system
How can we measure the distances between us and the various planets in the solar system? We can use a common reference unit, such as the distance from Earth to the Sun. But how can we estimate that distance? The history of these calculations stretches back at least as far as the scholars of antiquity!
GPS and shortest paths: Dijkstra's algorithm | Tangente
"At the roundabout, turn right": but how does our GPS find the shortest route to our destination?
What makes us human: geometric intuition | Tangente
Humans have possessed geometric intuition since the dawn of time—but do other primates share it? To find out, Mathias Sablé-Meyer proposes an experiment: identify the odd one out in a series of six quadrilaterals.
Marc-Antoine Mathieu: comics and dimensions | Tangente
Julius Corentin Acquefacques, prisoner of dreams, is perhaps the comic-book hero most often drawn into the world of mathematical ideas. Let's venture into the extraordinary world of his creator, Marc-Antoine Mathieu.
Rose Polymath and Anselme Lanturlu: Science comics | Tangente
Many comic-book authors draw on mathematics in their work, whether consciously or not. Conversely, scientists committed to public outreach who can also draw sometimes try their hand at making comics.
Donald in Mathmagic Land: finally in comic-book form | Tangente
Donald in Mathmagic Land (Hamilton Luske, 1959) is a 27-minute short film produced by Walt Disney Studios.
The n-queens problem
Did you enjoy "The Queen's Gambit"? Then you should like this problem.
An architect's dream?
The golden ratio, as everyone knows, crops up everywhere in art... provided, that is, you are determined to find it and willing to overlook (!) a few approximations or anachronistic units of measurement. Let's trace the writings that linked it to architecture and brought it to public attention.
Golden ratio in nature: fact or myth? | Tangente
The myth that the golden ratio is found in nature is remarkably persistent.
Golden ratio in art: between myths and realities | Tangente
However you look at the paintings, it is hard to substantiate the idea that the golden ratio's presence in art gives a work some decisive aesthetic quality. Let's see where φ really lurks...