Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Balls in the plane
A spherical ball is the set of points whose distance from a center is less than a constant. Mathematicians, always seeking to generalize, accept this definition of a ball… in any space equipped with any kind of "distance."
Convex geometry
Convex geometry lies at the crossroads of optimization, analysis, topology, combinatorics and, of course, geometry. The graphical and visual interpretations it affords are powerful aids to intuition. Yet fundamental questions remain open.
Optimizing consumption | Tangente
Making consumption choices is no easy matter. But for a rational consumer, the notion of convexity is extremely useful! Consumer theory provides a case in point here.
Surprising distances: Manhattan and Chebyshev | Tangente
The Euclidean distance in the plane is the one everyone knows: it tells us that the shortest path between two points is a straight line. But there are many others, often rather unusual. Some are downright surprising…
Maths on stage | Tangente
Over the past thirty years, forms of theatre have emerged that allow mathematics to be discussed, brought to life and shared. Artists and mathematicians, actors and directors alike have realised that there is a large and eager audience for such creations.
Revisiting the classics… | Tangente
Numerous shows with mathematical content are regularly created. But might there be mathematics in theatre itself? We can revisit the classics from a different perspective. Let's reread Molière, Marivaux and Ionesco.
So far, so near…
What is the distance between Paris and Rome? Faced with this question, one may legitimately wonder whether this means "as the crow flies," "by train," "by car," or "in the Euclidean sense." Ultrametric distances even reveal a world in which every triangle is isosceles.
The genesis of metric spaces
In the early 20th century, Maurice Fréchet and Felix Hausdorff felt they were discovering a new world: set theory provided the framework in which they introduced the concept of distance, a generalization of absolute value on the real numbers.
Coloring problems
How many colors are needed to color the plane so that no two points exactly 1 unit apart ever have the same color? Behind this apparently elementary question lies a problem that remains unsolved.
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.
A modern theory with ancient roots | Tangente
It was during the twentieth century that convexity emerged as a mathematical discipline in its own right. Before then, eminent mathematicians had occasionally glimpsed the potential value of this notion in geometry and analysis.
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.