Math for everyone
Mathematical content accessible to everyone
Voronoi cells | Tangente
How a London doctor used Voronoi diagrams to combat cholera.
Graphical statics
Have you heard of "graphical statics"? Rooted in mathematics, particularly geometry, it is the art of balancing the forces acting on a body… without any calculations. Surprisingly, the discipline originated long before vectors were introduced!
Lewis Carroll's diagrams
Lewis Carroll is known worldwide as the author of Alice's Adventures in Wonderland. Behind the pseudonym was Charles Lutwidge Dodgson (1832–1898), an Oxford mathematics lecturer with a passion for logic.
High-school reform: maths go off on a tangent | Tangente
Last January, the Société mathématique de France, together with several learned societies and professional associations, warned the Ministry about the disastrous effects of the new high-school reform on mathematics education. Here is an analysis, backed by figures.
Maths at home is good for the mind | Tangente
It is often assumed that differences in students’ academic success are explained by their parents’ level of education and ability to “help” them with their homework. New research supports other hypotheses.
My first differential equation | Tangente
Do differential equations frighten you? Admittedly, there is good reason to be wary. Yet they become very approachable once a few constraints are imposed; linearity is one of them. And when the factors involved are constants, they are within everyone's reach—especially when the right-hand side is zero.
2022 from every angle
Once again this year, the Tangente team has shown ingenuity in uncovering hidden properties of 2022…
Polls / Secrets of a "statistics machine"
Now that algorithms can analyze vast volumes of data, tools are being used to provide a comprehensive, concise overview of the information. The Hedwige aggregator, developed by the start-up Datapolitics, focuses on data from the world of politics.
Workshop of potential tragicomedy | Tangente
The Workshop of Potential Tragicomedy (Outrapo) is to theater what Oulipo is to literature.
Convexity in finance | Tangente
Mathematics plays an important role in finance. In recent years, returns on capital have been drastically reduced for various economic and political reasons. In Europe today, negligible returns on capital are becoming the norm, yet inflation remains very real, at around 5%.
Statistics and probability revisited
The basic statistical concepts of mean, standard deviation, median and median absolute deviation are widely used. We encounter them at school, in the media and in the workplace… All can be constructed from familiar distances, such as Euclidean or Manhattan distance.
Error-correcting codes: keeping errors at bay
When sending a message, it is important to ensure that it will still be understandable when it arrives, even if it has been altered along the way. That is precisely the role of error-correcting codes.
Norms on function spaces
The notion of distance can also be applied to functions
Surprising shapes in space
As in the plane, many balls associated with different norms can be defined in space. They include polyhedra, some regular and others more surprising. You can thus make a delightful festive collection of baubles to match your next Christmas tree!
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."
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…
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.