Everyday Math
Applied mathematics to everyday life: elections, sport, music, road traffic, weather, computer science, finance
RSA encryption explained by example | Tangente
RSA underpins the encryption of financial transactions.
Fermat's little theorem in practice | Tangente
Fermat's little theorem is used to test whether a number is prime. Here is how.
Psychological experiments in arithmetic
Like any other scientist, a mathematician makes use of experiments. But these do not necessarily resemble those conducted in other sciences: carried out mentally or on a sheet of paper, they are usually psychological in nature!
Naming the elements of a set
As David Hilbert famously remarked, assigning a name to a mathematical object is artificial. Identifying an object with its image under a bijection, however, so as to bring out its properties, can be decisive.
Relations and maps: structuring sets
A notion of relation between sets is essential if we are to begin doing mathematics. At the heart of the foundations of mathematics, the concept of a relation includes maps as a special case and gives sets structure.
Georg Cantor: from finite to infinite
To extend useful results about finite sets to infinite sets, Cantor defined equality of cardinalities in terms of bijections, and hence inequality in terms of injections and surjections. Remarkably, this yields an order relation.
Municipal grants: the maths that decide | Tangente
They are a key part of the budgets of municipalities and intermunicipal authorities. They are often calculated in rather strange ways, involving logarithms and the fifth power of the population!
Mathematical economics
Economists have often used percentages in their models
In economics too: maths at the heart of the system | Tangente
In economics, as in everyday life, rates are everywhere. Let's see how.
A practical protractor at last: measuring tools | Tangente
What could be more commonplace in geometry than a protractor?
Abolishing the baccalauréat: arguments and issues | Tangente
Created in 1808, the baccalauréat remained both an academic and a social landmark until the mid-20th century. It no longer plays that role, devalued by steadily falling standards and a rising but increasingly artificial pass rate. Should we not move on?
Straight lines in curved spaces: geodesics
If we restrict ourselves to a surface, the shortest path from one point to another is called a geodesic. This concept leads "straight" to non-Euclidean geometries and applications in navigation and cartography.
Mathematical vs astrological semantics | Tangente
Horoscope advice can seem sensible. Why is that? While advice in objective areas consists solely of tautologies, subjective advice draws on a multiplicity of meanings, allowing clients always to interpret it as they wish.
The beginnings of astrology
Astrology as we know it today is actually quite recent. It owes more to the Greeks of the Hellenistic and Roman periods than to the remote reaches of antiquity. Let us trace the history of practices often intended to determine the right moment for political decisions.
Salon 2016: maths transform our society | Tangente
The unmissable Salon Culture et Jeux Mathématiques will run from Thursday 26 to Sunday 29 May on Place Saint-Sulpice. Save these dates for the (free) mathematics event of the year!
Pierre Boulez, mathematics and glory | Tangente
"Music is a hidden practice of arithmetic, the mind unaware that it is counting," said Leibniz. Pierre Boulez, who died on 5 January, conductor, composer and teacher of music and musical composition all at once, revealed to the whole world the hidden face of "his" music, in which mathematics runs through like a watermark.
Root extraction
Newton's method is a general method for finding the solution to an equation of the form f (x) = 0 by applying a simple algorithm.
Richard Dedekind: Numbers and concepts
Richard Dedekind died on February 12, 1916. This gives Tangente an opportunity to profile a German mathematician fascinated by numbers, whose legacy continues to shape mathematics today. The concepts he introduced lie at the heart of modern algebra.
Adventurers of the forgotten pentagon: tiling the plane | Tangente
The recent discovery of a pentagon that tiles the plane brings to mind an endearing figure: Marjorie Rice. An American homemaker, she would hide away in her kitchen to indulge her passion for mathematics.
The choice of serve in tennis
A probabilistic model can help a tennis player choose which type of serve to use. Applied to the final of the last Davis Cup, which pitted Belgium against England.