Desargues meets Boy
Projective geometry is an important mathematical discovery that goes back to the work of Desargues in the XVIIth century.
Space filling curve
A space filling curve is a continuous map $\gamma \colon [0,1] \to \mathbb R^n$ whose range reaches every point in a higher dimensional …
Sylvester Machine
A Sylvester machine is a mechanical linkage realizing a directe similarlity . If the user sketches a figure with one pen, the other …
Pantograph
A pantograph is a device realizing a homothety. If a user draws a figure with one of the pens, the other pens will reproduce it dilated …
A paradox in high dimensional geometry
This “paradox” was explain to me by a colleague. Take a square whose side have length $1$ (on blue on the figure below) and …
Spheres in the Nil and Sol geometries
In his work on 3-dimensional manifold Thurston proved that there are exactly 8 “geometries” that serve as model for any compact three …
Fractals
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Platonic and Archimedean Solids
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Penrose tilings
The Penrose tilings is a quasi-periodic tilings. Every finite pattern that you can find will show up infinitely many times. …
Antoine’s Necklace
The Cantor set is one of the simplest fractal object. Its ternary representation is obtained by a recursive procedure: start with a …
Non Euclidean Geometries in Virtual Reality
The Uniformization Theorem of complex analysis tells us that there are three important two-dimensional geometries: hyperbolic, …
Double Pendulum
A (single) pendulum is a standard object studied in every mechanics textbook. Its tidy behavior is advantageously used to punctuate …