

Mathematical modelling offers one way to make sense of Vanuatu's sand drawings. In particular, it will lead us to a surprising "turtle theorem".



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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.

Maryam Mirzakhani is also known for having obtained, with Alex Eskin and Amir Mohammadi, the magic wand theorem, so named because it made it possible to solve at a stroke many previously inaccessible problems. To explain it, let's first delve into translation surfaces. The illumination problem is one of its many applications.

What do links and planar graphs have in common? They are connected by a relationship that associates a graph with any given link and, conversely, provides a simple way to encode—and therefore draw—any link using a graph.

Can a polygon be cut from a sheet of paper with a single straight cut? Surprisingly, the answer is yes! More surprisingly still, this also applies to other objects.
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