Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
With a straightedge alone... or almost
According to the Poncelet–Steiner theorem, every straightedge-and-compass construction can be carried out with a straightedge alone, provided that a fixed circle and its center are given. But how is this done in practice? Though the question may seem playful or even pointless, it has in fact attracted the attention of several mathematicians.
The builders' geometric constructions
Several centuries before the Renaissance, whether building a church or a fortress, builders needed only a compass and an unmarked straightedge to draw arcs, pointed arches, basket-handle arches and rose windows. Let us explore the basic geometry behind their methods.
Straightedge and compass in education
How long have schoolchildren been drawing geometric figures with a straightedge and compass? More importantly, why? Even elementary geometric constructions must be introduced progressively, and this requires knowledge to be organized systematically.
Bernard Cornet's geometric art and Voronoi | Tangente
In art, mathematical tools can help artists develop and create their work. The Nantes painter Bernard Cornet (born in 1952) has brought Voronoi diagrams and Delaunay triangulation into his artistic practice.
Dynamic geometry in action with GeoGebra | Tangente
Developed in 2002 by an Austrian student, GeoGebra is an educational tool with an unusual history. Designed for mathematics teachers worldwide, it is especially popular among secondary-school teachers in France. Tangente spoke with the software's creator, Markus Hohenwarter.
Origami and folds for geometric constructions
Greek geometers regarded only straightedge-and-compass constructions as acceptable. Some problems that defeated their ingenuity—for reasons that would not be understood until the advent of algebra—can nevertheless be solved using origami.
Triangles with an angle trisector that is a median
A geometric question about trisecting an angle can lead to some astonishing discoveries! Along the way, we encounter triangles, angle trisectors that are also medians, the non-constructible 20° angle—and curves not yet catalogued?
Circles in ancient Roman mosaics | Tangente
Besides their undeniable aesthetic appeal, mosaics and other archaeological remains from our past often hold wonderful mathematical surprises. These geometric examples from Gallo-Roman sites offer ample proof.
From geometry to algebra: constructing numbers
Starting with two distinct points in the plane and performing only finitely many ruler-and-compass constructions, can we obtain any point in the plane? If not, which points can we obtain in this way?
The parabola in all its finery | Tangente
A common exercise in the days of descriptive geometry was to construct a point on a curve and its tangent. Following the ellipse, here is a short survival guide offering a handful of constructions for solving the same problem for the parabola.
The ellipse and its many features
Although descriptive geometry provides laborious methods for constructing an ellipse with straightedge and compass (see the article "Albrecht Dürer and technical drawing"), other, more conventional methods also exist. A point on the curve, the center, foci, axes and tangents: let's take a quick tour of the available techniques!
When the compass won't follow the ruler
A famous result in geometry, still surprising when first encountered, states that any point in the plane constructible with straightedge and compass can be constructed with a compass alone. But how is this actually done?
Albrecht Dürer and technical drawing | Tangente
Albrecht Dürer (1471–1528) devised a fascinating straightedge-and-compass construction of the ellipse. It foreshadowed descriptive geometry, which Gaspard Monge (1746–1818) would formalize almost three centuries later.
Enter the Tangente Prize for best article
The 2021 Tangente Best Article Prize is now open! Why not put pen to paper?
Let’s bite into maths: 2021 Fair | Tangente
Get a first glimpse of the programme for the 22nd Culture and Mathematical Games Fair. Held online, it will be accessible to everyone, from anywhere.
Math City Map: Math trails | Tangente
If, by chance, you ever find yourself confined to within 10 km of your home, you can always turn the restriction to your advantage by creating mathematical challenges in your local area.
Math tourism: mathematics, geography and travel | Tangente
For some fifteen years, the "math tourist" website (mathouriste.eu) has been sharing photographs from Alain Juhel's mathematical travels and visits to places connected with mathematics and mathematicians.
Portraits of women mathematicians | Tangente
To honor Maryam Mirzakhani, International Day of Women in Mathematics is observed on May 12, her birthday.
Roman numerals and modern passions | Tangente
Controversy in Lutetia, in March MMXXI. The Carnavalet Museum, devoted to the history of Paris, has allegedly "abolished Roman numerals" from its new visitor experience on the pretext that they represent "an obstacle to understanding", claims the Italian daily Corriere della Serra.
Alan Turing on the £50 note | Tangente
On June 23, 2021, Alan Turing (1912–1954) would have turned 109. To mark this symbolic date, the Bank of England will issue a new £50 note (about 58 euros) bearing the scientist's portrait.