Geometry
Explore mathematics articles on the theme of geometry.
Mercator projection: anatomy of a geopolitical map
We tend to think of mathematics as a perfectly neutral science. Yet, like any human construct, its uses can prove more political than they appear. That is how an age-old geometry problem found its way into diplomatic debates in recent months.
Regular polygons with integer-coordinate vertices: one proof for all n
Discrete geometry is a recent field of research concerned with "discrete objects," such as graphs and tilings. But it also offers a fresh perspective on problems that are difficult to solve in a continuous setting, including the existence of regular polygons with integer-coordinate vertices.
Integer points on a line: methods of solution
Many problems in discrete geometry are simply stated and can be used in teaching to make certain concepts easier to understand. Searching for points with integer coordinates on a line naturally leads to applications of theorems from number theory.
Moving on the discrete plane: generating sets and minimality
Exploring how one can move around a grid leads to the concepts of generating sets and minimality. This example shows the power of discrete geometry as a tool for better visualizing and exploring complex ideas from classical geometry or algebra.
Discrete lines: the birth of a new geometry
Problems involving representation on a pixelated screen belong to discrete geometry. But beyond mere aesthetic considerations, are these new subjects of study—including discrete lines—tools for exploring Euclidean geometry more deeply, or objects of a new geometry?
Patrice Jeener: the mathematical engraver who turned equations into art
Patrice Jeener (1944–2026) passed away on March 3 in his village of La Motte-Chalancon, in the Drôme.
Theaetetus and the diagonal: why stop at √17?
How should we understand the famous passage in the Theaetetus where Theodorus mysteriously stops at the square root of 17? A new hypothesis emerges, involving continued fractions and triangular numbers.
Cédric Aubouy, math clown and author of “Je ne sais pas”
Cédric Aubouy, a mathematical clown and founder of the L’île logique company, agreed to meet us to mark the publication of his first novel, Je ne sais pas ou la disparition des mathématiciens.
Euler–Cramer paradox: Are 9 points enough to define a cubic?
The Euler–Cramer paradox: If nine points seem sufficient to determine a cubic curve, how can two distinct cubics also pass through those same nine points?
Gabriel Cramer and Cramer's rule in the 18th century
The appendix to Gabriel Cramer's Introduction à l’analyse des lignes courbes algébriques contains the famous rule for solving systems of linear equations and Bézout's theorem.
Plotting algebraic curves in the 18th century: Newton’s and Cramer’s analytic methods
How did Gabriel Cramer plot algebraic curves in 1750? Discover Newton's analytical parallelogram and Cramer's analytical triangle.
Gabriel Cramer: the journey of an 18th-century Genevan mathematician
Explore Gabriel Cramer's journey, from his education in Geneva to his European Grand Tour among the leading mathematicians of his day.
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.
What makes us human: geometric intuition | Tangente
Humans have possessed geometric intuition since the dawn of time—but do other primates share it? To find out, Mathias Sablé-Meyer proposes an experiment: identify the odd one out in a series of six quadrilaterals.
Rose Polymath and Anselme Lanturlu: Science comics | Tangente
Many comic-book authors draw on mathematics in their work, whether consciously or not. Conversely, scientists committed to public outreach who can also draw sometimes try their hand at making comics.
Donald in Mathmagic Land: finally in comic-book form | Tangente
Donald in Mathmagic Land (Hamilton Luske, 1959) is a 27-minute short film produced by Walt Disney Studios.
Phi is irrational: a geometric proof | Tangente
Let's see how to prove that φ is irrational.
Poincaré conjecture in manifold topology | Tangente
By the end of the 19th century, following the work of Poincaré and many other mathematicians, including Bernhard Riemann (1826–1866) and Enrico Betti (1823–1892), the topology of surfaces in our ordinary space was well understood.
Convex sets and line segments | Tangente
It is fairly easy to tell whether or not a subset of the plane is convex.
The magic ring of tetrahedra | Tangente
Details on how to build the ring of tetrahedra that you can cut out from the pull-out section of Tangente 200. An explanation of how the numbers on its forty faces were chosen, using a rule that generalizes the concept of a magic square.