Geometry
Explore mathematics articles on the theme of geometry.
Computer geometry: Cabri and GeoGebra | Tangente
Although computer drawing had been possible since the 1970s, so-called "dynamic geometry" software did not become widespread until the 1980s.
Compass: a universal instrument | Tangente
Compasses are made of wood or metal, in all sizes, with or without a sector.
Why a sound method matters in geometry | Tangente
Never known how to "get started" on a straightedge-and-compass geometry problem? What matters, which points should you introduce, and which line should you construct? The classic, tried-and-tested method of analysis and synthesis provides a sound approach to such construction problems.
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.
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.
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.
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.
The artist and the number: art and maths | Tangente
Mathematics in general, and numbers in particular, have inspired many artists, including Dalí and Picabia. Some are drawn to the magic of numbers. Others find beauty in number sequences, which they bring to life in graphic art or painting.
Mapping with Khartis: visualization | Tangente
Most data visualizations in the press are created with this open-source software, developed since 1995 by the mapping workshop at the Institut d'études politiques de Paris ("Sciences Po").
Teja Krašek in Escher's footsteps | Tangente
Born in Celje, Slovenia, Matjuska Teja Krašek (pronounced "Teyla Krashek") lives and works in Ljubljana. Her work draws on her fascination with symmetry, fractals and, more broadly, the beauty she sees in mathematics. She agreed to share her passion with us.
Squares in art | Tangente
Several artists have taken an interest in the square in order to explore its geometry
Three unsolved problems in geometry | Tangente
Geometry abounds in problems that remain unsolved. Some date back to the Renaissance! In tribute to Richard Kenneth Guy (1916–2020), here are three, gleaned from his book Unsolved Problems in Geometry (with Hallard Croft and Kenneth John Falconer, Springer, 1991).
Penrose takes center stage to kick off 2021 | Tangente
To mark the award of the 2020 Nobel Prize in Physics to Sir Roger Penrose—a mathematician well known for his work in cosmology, differential geometry, tilings and science communication—Tangente is shaking up its schedule!
Computational geometry: key challenges | Tangente
It is easy to overlook, but many geometric problems can be solved by iterative methods or, more broadly, algorithms. These questions are the subject of computational geometry! This is a vibrant, highly active field in which many seemingly elementary questions still await solutions.
Would you like a slice of a sphere? | Tangente
John Conway passed away this year, but the profound questions he raised across many fields remain as relevant as ever (see Tangente 194).
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.
Welcome to the world of virettes: Lissajous curves | Tangente
Marcel Guery explores the artistic potential of Lissajous curves
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.