Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Euclid, master of division
With the Greek mathematicians—Euclid in particular—numbers moved from the concrete to the abstract. One key concept endured: Euclidean division and the host of developments it spawned. These methods have not aged a bit: Euclid's algorithm is still used today... by computer scientists!
Number theory in 2016: a wealth of news | Tangente
An unexpected bias in the distribution of prime numbers has just come to light. At the same time, Andrew Wiles receives the Abel Prize.
APB software: post-bac placement algorithm | Tangente
A software program assigns students who have just passed the baccalauréat according to their preferences. But the opacity of how it works leaves room for a number of concerns.
Porto: in Gomes Teixeira's footsteps | Tangente
When we think of Porto, we think of its wine, its river and bridges, or the much-missed filmmaker Manoel de Oliveira. We never think of its mathematician, Francisco Gomes Teixeira Costa! Let's revisit the Portuguese city by following in his footsteps.
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?
The Liouville Journal: a key mathematics publication | Tangente
In 1832, the Annales de mathématiques pures et appliquées, better known as the Annales de Gergonne, ceased publication after twenty-two years.
Heine and the rigorous study of continuous functions | Tangente
Eduard Heine is not among the best-known mathematicians, even though his name is attached to a theorem on the uniform continuity of continuous functions on a closed interval.
On the trail of a forgotten book: 19th-century textbooks | Tangente
The Éléments de trigonométrie rectiligne (Elements of Rectilinear Trigonometry), written by a mysterious F.J., were found in the trash of a religious institution in Damascus in the early 1990s.
From Euclid to Bourbaki: perpetual reform
Mathematics has undergone waves of reform in the past, is undergoing them now, and will continue to do so. This applies to schools of mathematical thought and major research movements, but also to elementary mathematics—the mathematics taught in secondary schools in most countries around the world.
Above all, let's keep the baccalauréat: in defence of a republican examination | Tangente
It is easy to yield to the siren song of those who discredit the baccalauréat to make it easier to abolish. Yet a majority of people in France want to preserve this symbol of "republican elitism".
GCD algorithms: comparing calculation methods | Tangente
The algorithm for computing the GCD dates back at least to Euclid. It was subsequently refined over the centuries.
Divisibility criteria: history and methods | Tangente
You know the divisibility criteria for 2, 3 or 5 — but do you know those for 11 or 25?
The scant remainder of Euclidean division
When we divide a by n using Euclidean division, we obtain a remainder. This remainder can take only a limited range of values: there are just n of them. This new perspective can simplify many calculations and cast a whole host of problems in a different light!
Division algorithms
From the abacus to the counting frame, what a long way we have come to reach our present-day algorithm, so well known to schoolchildren.
Mathematician and pianist: a winning composition | Tangente
The final of the 27th international competition for great amateur pianists, bringing together 92 candidates from 27 different countries, took place on April 10 at the grand amphitheater of Assas in Paris.
Drawing a line on a computer
What could be simpler than drawing a line between two points? All you need is a ruler and a pencil! But how do you do it on a computer screen? How does graphics software manage it? The task is to turn certain points on the screen black. But which ones?
The projective line: a fruitful new perspective
The line is the simplest geometric figure imaginable. The variety of situations encountered in geometry may seem more complicated, and yet… might there be a special perspective from which the plane could be understood as a line? That is precisely what projective geometry is about!
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.
Tangents and asymptotes
From yesterday's "touching line" to today's tangent, from "vanishing quantities" to asymptotes, the story has been a long mathematical epic. Here are a few glorious episodes from this geometric quest to "approximate curves with straight lines."
Caustic envelopes
Lines whose direction varies continuously may reveal the curve to which they are all tangent. Such curves, enveloped by straight lines, appear in optics as caustics. Their properties give rise to geometric construction methods.