Imagine
Inventing the nonexistent, exploring unknown worlds, moving "differently"... Surfaces allow theorists to let their imagination run free, to build, for example, objects of a new kind that help understand the trajectory of a billiard ball. Nothing stops creativity, which even goes so far as to explain, with "smooth fractals", how to fit the Earth inside a balloon or a thimble... Mathematics today leads to real miracles!
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The epic of non-Euclidean geometries | Tangente
In antiquity, Euclid essentially postulated that, given a point A and a line D, there is exactly one line through A parallel to D. Two millennia later, three mathematicians share the glory of having proved that a geometry could exist without this "fifth postulate".
The smooth fractal revolution
How can a sphere be made to occupy less volume? Or how can an object be brought from the fourth dimension into the third? The corrugation technique meets such geometric constraints and produces surfaces both strange and unprecedented: "smooth fractals."
Remarkable mathematical surfaces | Tangente
In search of the missing squares | Tangente
There is no need to invoke the paradoxes of infinity to have fun with areas: a simple rectangle is enough to create some formidable puzzles! All you need is a sheet of paper, some pencils, a ruler and a pair of scissors—and you are ready to make little squares disappear.
Operations in billiards
One of the arts and pleasures of mathematics is finding different ways to represent problems. Some problems in dynamics can profitably be replaced by the study of trajectories on a billiard table, revealing hidden structures—and hence hidden logical beauty.