Topology, deforming without tearing
When an elastic object can, when it is deformed continuously without tearing, take the shape of another object, they have the same topological structure: they are said to be homeomorphic. A sphere and a cube (both hollow) are homeomorphic, but they are not with a torus. Topology provides a fundamental complement to analysis and to the definitions of limit or continuity by introducing new notions such as compactness. Welcome to this geometry "unlike any other"…
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Untangling the mysteries of rubbery deformations
The metric properties of modelling-clay objects change when they are deformed. Other properties, known as topological properties, remain unchanged. Surprisingly, algebra enters the picture. This naturally leads us to consider knots and the constituent molecules of DNA.
The story of a geometry unlike any other
A science that is hard to define in a few words, topology has found its way into geometry, analysis and even algebra. How did it emerge in the mathematical world? Where is it useful? And above all, what is topology? Let's look back at the birth of a new way of seeing our space…
This is not a Möbius strip! | Tangente
Think you know everything about the Möbius strip, topology's quintessential object? Think again! Paper models of it have thickness, which undermines some of their properties. Let's explore these subtleties.
Knot theory according to Jean-Michel Othoniel | Tangente
Jean-Michel Othoniel is an original sculptor in more ways than one. His exhibition "Géométries amoureuses" was held in Sète (Hérault) in 2017, and his current exhibition "Face à l'obscurité" has just closed at the MAMC in Saint-Etienne (Loire).
Coloring the plane: when geometry gets involved | Tangente
For plane coloring, we already knew that four colors were enough to color any map so that no two neighboring countries ever had the same color.
The Klein bottle
The bottle named after Felix Klein is a classic of topology, yet its mathematical properties are still sometimes poorly understood. Let's delve beneath the surface to uncover its connection with the Möbius strip.