Mathematicians like to create amusing puzzles, for example, 'geometric dissections'. By cutting a geometric shape into pieces and then rearranging them, they seek to create another shape with the same area (surface).
The Chinese game of Tangram, which you may be familiar with, works on the same principle. Mathematicians have even determined, through clever calculations, that between two geometric shapes (polygons) of the same area, there is always a way to cut one to recreate the other.
As they also like to makes things more complicated, they have even invented a game where the shapes must be additionally connected to each other by hinges. This is what they call 'hinged dissections'.
Here is a a nice example showing how a square can become a triangle and vice versa.
This project was developped for the magazine 'Campus Junior' of the University of Geneva.