Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
When maths divides economists | Tangente
Over the past few decades, several disputes have punctuated relations between economists and mathematicians.
From derivatives to elasticity
It is often useful to study the relationships between different economic quantities. One such question is how the quantity demanded of a good depends on its unit price…
When economics illustrates matrix algebra
Economists' data can often be arranged in rectangular tables that can be manipulated according to precise rules tied to the mathematical concept of linearity. Matrix algebra can thus be illustrated with concrete examples drawn from economics.
The poverty threshold
Most developed countries have policies to help the poorest members of society. This raises the question of what we mean by "poor." Should the definition be absolute or relative? Should it refer only to income, or should assets and place of residence also be taken into account?
Understanding gross domestic product
There are many ways to measure a nation's wealth. Calculating gross domestic product is one of them, but other, complementary indicators are also used.
Antoine Cournot: from mathematics to economics
Economics did not always have much to do with mathematics, and for a long time its reasoning was verbal, until the arrival of thinkers such as Antoine Cournot, who brought rationality into the field in the 19th century.
The Bauhaus between art and science: geometry and creation | Tangente
Right now, several exhibitions in Paris and elsewhere in France are not to be missed
A taste for maths: events programme | Tangente
The City of Paris libraries are devoting their 2017 programme, particularly in January and February, to the world of mathematics
Optimization problems in mountainous terrain
Geometrically, optimizing a function of two variables means locating special points on its graph: the "highest" and "lowest" points. This search can be illustrated by exploring a… mountain landscape.
The geometer's art
Geometry has its secrets: it often allows us to solve extremum problems without resorting to analysis or algebra. It also gives us an opportunity to revisit some classic results in triangle geometry.
Other optimizations: PERT and beyond | Tangente
Optimization techniques are sometimes hidden in other subjects. Here are a few examples
Imre Lakatos and mathematics education | Tangente
The Hungarian mathematician Imre Lakatos set out his perspective in his best-known work, Proofs and Refutations. He illustrated his argument using Euler's formula.
Following in Euler's footsteps
Euler's formula has led to many further developments, including its use in the study of polytopes.
OuLiPo: Mathematics inspires literature | Tangente
On November 24, 1960, Raymond Queneau, a writer with a passion for mathematics, and François Le Lionnais, a mathematician with a love of literature, founded Oulipo (the Workshop of Potential Literature), together with mathematicians such as Paul Braffort and Claude Berge, as well as Jacques Bens, Jean Lescure and Marcel Duchamp. They would later be joined by Georges Perec, Luc Étienne, Jacques Roubaud, Italo Calvino and others.
Analyzing an alien language: mathematics | Tangente
Extraterrestrial spacecraft hover above Earth. A linguist (played by Amy Adams) and a scientist (Jeremy Renner) are tasked with asking the aliens about their intentions.
The mathematical geometry of Turkish | Tangente
Turkish is an agglutinative language, using suffixes to form its various grammatical features: declension, possession and conjugation. Projections onto a cube determine which suffix to use.
No derivatives required: optimization for everyone!
Optimization and differentiation are linked—but in both algebra and geometry, derivatives can sometimes be avoided. A few elementary algebraic examples will show us that quadratics are often subtler than they look…
An illustrious line of descendants
It all began with a football to which Euler's formula was applied. Why does the constant 2 appear on the right-hand side? To find out, we follow in the footsteps of Henri Poincaré, André Weil and… Alexander Grothendieck.
The pursuit of Euler's formula for polyhedra | Tangente
In a polyhedron, the number of vertices, S, plus the number of faces, F, equals the number of edges, A, plus 2. In other words, S + F = A + 2. For many mathematicians, Euler's formula is the most beautiful formula of all! Above all, it has had an eventful history, to say the least...
Formal languages and automata
What do a dictionary, a computer program and the DNA in our cells have in common? Language! A deterministic finite automaton is a useful practical tool for working with this concept. But the limitations of these abstract machines soon become apparent…