

Constructing a parabola is both fun and highly instructive. It brings its geometric properties to life and even provides an opportunity to do some arithmetic.



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Every regular curve is the envelope of all its tangent lines. For conics, these tangent lines are particularly easy to construct geometrically, making it possible to produce them by folding.

In art, mathematical tools can help artists develop and create their work. The Nantes painter Bernard Cornet (born in 1952) has brought Voronoi diagrams and Delaunay triangulation into his artistic practice.

Straightedge-and-compass geometry boasts a long history. But Euclid and his followers do not have a monopoly on points, lines and figures! The study of origami geometry is more recent, and it is surprisingly effective. Kazuo Haga has shown just how much richness a simple fold can hold.

Some constructions impossible to achieve with straightedge and compass become possible using origami… but not all of them! Paper folding also lets us revisit several questions of concurrency or collinearity, and reflect on the construction of polygons.
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