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Dive into the fascinating world of mathematics with our captivating articles, written by passionate experts. Whether you are a curious amateur or a seasoned mathematician, our articles cover a wide range of topics, from fundamental concepts to the latest discoveries, including practical applications and philosophical reflections.
Counting in Chinese: numeral systems and counting rods | Tangente
The Chinese numeral system dates back to the beginnings of written Chinese, around the third millennium BC.
Translation and transcription of Chinese texts | Tangente
Translating and transcribing writing systems and pronunciations very different from our own requires us to clarify certain conventions and practices.
Editorial
To discover the mathematics of other places and other times is to immerse oneself in an otherness that we often tend to flatten under the weight of a few received ideas picked up here and there. In our special issue no. 93, we set out to discover mathematics in the lands of Islam; this time, we travel to the Far East. These destinations open some of the most beautiful doors of our imagination: China, Japan and Korea.
The return of Hex | Tangente
Hex is a two-player game played with black and white pieces on a diamond-shaped board tiled with hexagons. The first player to connect their two opposing sides with their pieces wins.
New geometric volumes... | Tangente
In a recent study published in the Notices of the American Mathematical Society, mathematicians Claudia Fevola (Inria Saclay) and Anna-Laura Sattelberger (Max Planck Institute in Leipzig) explore the emerging field of positive geometry to propose a novel bridge between particle physics and cosmology.
Three cheers for France! | Tangente
The international final of the Mathematical and Logic Games Championship was held on August 23 and 24. This year, it took place in Mahdia, Tunisia.
Making art with the Conway knot | Tangente
An artist passionate about mathematics, Michel Delaunay creates works that plunge the eye into the infinity of geometric and topological aesthetics. He notably combines the potentialities of the cube with those of the Conway knot.
Saint-Simon's dream of a mathematized... | Tangente
In 1820, Saint-Simon proposed a complete reorganization of political life in which he imagined handing power to mathematics. Although his project was never implemented, it directly influenced the emergence of technocracy and our conception of expertise in politics.
Roger Mansuy's mathematical almanac | Tangente
On the occasion of the publication of his Grand almanach mathématique (The Grand Mathematical Almanac), Roger Mansuy opens up to Tangente about the secrets of this book like no other, in which readers discover, among others, many unjustly forgotten figures.
In real life | Tangente
In physics as in architecture, parabolas often appear, whether to model phenomena or provide inspiration.
Celestial parabolas | Tangente
Imagine the Solar System as a collection of different bodies—planets, comets…—subject only to the Sun’s gravitational pull. Classical mechanics then tells us that their orbits can trace only three types of curve: ellipses, hyperbolas and parabolas.
Straightening the curve
The quadrature of the parabola was one of the first triumphs of ancient geometry in the study of areas bounded by curved lines — a success wrested through fierce struggle by Archimedes, before more modern methods simplified and generalized the result.
Tangents and the parabola: gems galore
Behind its sleek appearance, the parabola brims with fascinating properties. Thus, the study of its tangents reveals remarkable angular properties and offers a playground of astonishing richness, where classical geometry meets luminous reflections.
From Pascal to Poncelet
In the winter of 1812, the retreat from Russia ended in disaster. Jean-Victor Poncelet (1788–1867), a 24-year-old military engineer, was taken prisoner. Steeped in Gaspard Monge's (1746–1818) descriptive geometry, he laid the foundations of modern projective geometry in the prison camps of Saratov, without books or instruments.
Constructing a parabola | Tangente
Constructing a parabola is both fun and highly instructive. It brings its geometric properties to life and even provides an opportunity to do some arithmetic.
A line, a point, that's all | Tangente
The parabola is one of the simplest curves to define, yet also one of the richest, with properties that make it a flagship object in classical geometry as much as in algebra and analysis. It thus offers an opportunity to bring together different mathematical perspectives.
Misleading graphical proofs: the missing square paradox and more
Discover how seemingly rigorous diagrams can fool us: the missing square paradox, the astonishing proof that every triangle is equilateral, and more.
When Legendre believes he has proved the fifth postulate
For two millennia, mathematicians sought to prove Euclid's fifth postulate. Adrien-Marie Legendre believed he had found a proof, before realizing that his proof implicitly assumed the truth of that same postulate. A circular argument…
Misunderstanding Indian numerals | Tangente
Indian numerals passed through Islamic lands as early as the eighth century (see Tangente special issue 93), then naturally made their way to Spain. There was just one problem: in the medieval West, zero was systematically left out! This failure to grasp the decimal positional system would cause a delay of a good century and a half…
A shaky proof revolutionizes arithmetic
Euler rescued from oblivion Fermat's proposition that it is impossible for the sum of two cubes to be a cube. Though the explanation he provided for it was shaky, it opened up a new framework for arithmetic.