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Hinged dissection

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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.




Cut three squares of 16 cm × 16 cm in corrugated cardboard.   Glue them together.   Let it dry.
On one side of the square, draw the 3 blue lines as shown on the diagram.   Use a ruler to be ...
With a cutter and a ruler, cut straight along these 3 lines to create 4 shapes.
Cut out three small strips of bristol the thickness of the square and 2 cm long.   Fold them i ...
Glue the three hinges as indicated in the step 2 diagram with small circles
Once the glue is dry, you can unfold the square and turn it into a triangle as shown below.   ...