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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.
Coronavirus Polymath project | Tangente
The mathematical community is joining the fight against the pandemic.
The 93: Covid hotspot or bad math? | Tangente
A figure published by the Institut national de la statistique et des études économiques (Insee) and picked up by the media painted a catastrophic picture of public health in Seine-Saint-Denis (93).
Essential mathematics references | Tangente
The Mathcurve website is essential reading for anyone interested in curves. Several major authors are also closely associated with the subject.
Drawing machines: building mathematical curves | Tangente
Viewed as geometric loci, curves have always been drawn on a physical surface using instruments—or even machines. The mechanical linkages devised for this purpose can faithfully reproduce the curve under study.
Graceful roulettes: epicycloids and cycloids | Tangente
Drawing paper, tracing paper, colored pencils, a little curiosity and some practical ingenuity... You now have everything you need to explore roulettes and rediscover a now-forgotten classic of dynamic geometry: plane-on-plane motion.
Wheels and roads to match
Surprisingly, wheel and road profiles can be tailored so that the wheel’s axle remains at a constant height, ensuring maximum comfort for the traveller.
Mary Everest Boole, a surprising educator
Mary Everest did much to advance mathematics education. Among her innovations were the thread boards she used to make curves tangible.
Triangle cubics
Beyond the centroid, the orthocenter and the centers of the two circles familiar from school geometry, thousands of points can be associated with the three vertices of a triangle. These myriad points lie on hundreds of cubics with remarkable properties.
Welcome to the world of virettes: Lissajous curves | Tangente
Marcel Guery explores the artistic potential of Lissajous curves
Parabolas and catenaries
The parabola and the catenary are two grand dames of geometry, both with the same open U-shape. The first was studied by the Greeks 2,500 years ago; the second, "only" 330 years ago, by 17th-century mathematicians.
Curves that go beyond the compass
Even when some "natural" problems prove impossible to solve, mathematicians have found ways around them, producing approximations of varying accuracy. To do so, they have sometimes had to draw on a host of geometric tricks and devise ingenious mechanisms.
Deflecting an asteroid with mathematics | Tangente
An international team is tasked with studying the possibility of deflecting the trajectories of asteroids if there is a risk of collision with Earth.
Improving the 200 m record with maths | Tangente
What if speed records could be improved by changing the shape of athletics tracks?
The Anosov flow takes center stage | Tangente
What is the mathematical meaning of the magnificent image on the cover of Tangente special issue 74, Courbe et surfaces?
The endless variety of glissettes | Tangente
Roulettes do not exhaust the possibilities offered by plane-on-plane motion—or the geometric wonders hidden within it. Armed once again with drawing paper, tracing paper and pens, we continue our exploration with some somewhat overlooked curves: glissettes.
Generating CAD curves with Bézier | Tangente
Computer-aided design (CAD) emerged with the first computer graphics systems in the field of industrial design. Geometric design algorithms underpin 3D representation.
Elliptic curves
An elliptic curve is an algebraic curve of genus 1, defined by a polynomial equation in Cartesian coordinates with real coefficients.
An algebraic stroll
Algebraic curves come in every degree and every variety. They can be represented in the real plane, the complex plane or even the projective plane. How can we find our way around? Learn to recognize them and navigate this rich geometric universe!
Curves that leave the plane
Not all curves in space are confined to a plane. To study these "space curves," several new concepts—curvature and torsion—are introduced using a carefully chosen frame of reference. Get to grips with them and learn how to use them!
Getting to grips with polar coordinates
Polar coordinates are particularly well suited to plotting and studying circles, rose curves, and other spirals.