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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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 …