Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Different types of tangency in microeconomics | Tangente
In microeconomics, certain arguments rely on a graphical representation and call upon different types of tangency. This is the case with basic consumer theory, the Edgeworth box, and a firm's long-run average cost.
When waves go off on a tangent
Whether reflecting sound or waves, parabolic reflectors rely on the properties of tangents to conic sections. Let's fully dissect the underlying geometric phenomenon exploited in the making of antennas of every kind.
Tangent or asymptote?
Confusing "tangent" and "asymptote" is a very common mistake: what student has never made it? Yet the distinction between the two notions is perfectly clear. An exploration of certain constructions in projective geometry will nonetheless force us to call our certainties into question.
Deviation of a curve from a tangent
Newton and Leibniz, the founders of differential and integral calculus, studied how a curve deviates from a tangent. To this end, they drew on the notion of curvature. The fundamental ideas of these two scholars gave rise to contemporary mathematical analysis.
Observing curves with magnifying glasses
Used appropriately, extremely powerful magnifying glasses make most curves appear to coincide locally with a tangent line or an osculating circle.
Beyond Descartes
Several results in the plane and in space generalize Descartes' theorem on the curvatures of tangent circles.
Touching circles
Euclid's Elements, the standard reference for centuries, established straightedge-and-compass proof as the norm in geometry. But many problems involving circles tangent to one another become simpler when using conics or transformations, such as the indispensable inversion.
The Malfatti circles in a triangle | Tangente
In a triangle, how should three non-overlapping circles be chosen so as to minimize the area of the triangle left over once the three circles are removed? A natural solution, involving tangents within the triangle, is not the best one, but it gives rise to interesting problems.
The arbelos
The properties of the arbelos, this fascinating geometric object studied since antiquity, are countless. How did the Greeks go about establishing such results? Let's look at a few clues, drawing on the texts handed down to us by Archimedes and Pappus.
A theorem puzzle in pictures: Monday's challenge | Tangente
Since 2015, the Image des maths website (https://images.math.cnrs.fr) has featured a "picture-theorem puzzle" every Monday, taken from Geometry in Figures, a book published in 2011 by the young Russian mathematician Arseniy Akopyan (CreateSpace Independent Publishing Platform) and available in French as Figures sans paroles (Independently Published, 2019).
Pitot's theorem for quadrilaterals | Tangente
First stated by the French engineer and physicist Henri Pitot (1695–1771), the theorem that bears his name concerns quadrilaterals with an inscribed circle (known as tangential quadrilaterals).
The tangent at X: École Polytechnique slang | Tangente
The right to wear a sword, formerly reserved for sergeants, was not granted to students at the École polytechnique until after the three revolutionary days of July 1830.
A little terminology
When discussing tangency, it is important to keep a few basic definitions and properties in mind, especially when tackling somewhat elaborate constructions…
Yitang Zhang's long, solitary quest | Tangente
Born in China in 1955, Yitang Zhang developed an interest in mathematics at an early age: at the age of 10, he discovered prime numbers and the puzzle of Fermat's Last Theorem. But during the Cultural Revolution, he was sent to work in the countryside with his mother and was unable to continue his studies.
What neurologists think | Tangente
It seems widely accepted that our faculties diminish with age. What about our capacity to do mathematics? What can neuroscience specialists teach us about this?
The factorization of large integers:
The most widespread cryptography system relies on the use of very large integers, whose factorization remains beyond the reach of our computers. As early as the 17th century, Mersenne and Fermat were investigating the prime factorization of very large numbers; their work inspired modern factorization algorithms.
The second life of women mathematicians | Tangente
There is no shortage of examples of mathematical careers extended to a relatively advanced age, or begun late in life. The few women who, throughout history, managed to produce fine results despite every obstacle, often find themselves in one of these situations.
Mathematicians to the last breath! | Tangente
Mathematical creativity seems to wane with age. Few results of real importance have been proved after the age of 50. Yet some mathematicians defy this prejudice, pursuing fruitful scientific work right up to their last breath. So what is their secret?
Tangente's 35th anniversary | Tangente
Come celebrate a unique anniversary, the 35th anniversary of the only magazine of mathematical culture in the world sold at newsstands! There will be something for every taste, every age and every level. Here is a preview of what this eventful day has in store. The full program can be found at the end of this article.
Tangente Day 2023 at the Musée des Arts et Métiers | Tangente
Come celebrate the Trophées Tangente day, the world's only magazine of mathematical culture sold at newsstands! There will be something for every taste, every age and every level. Here is a preview of what this full day has in store.