TANGRAM: a brain game from legend

 

The Tangram Legend 

The legend says: “Thousands and thousands of years ago, Yu, the Great Dragon, lived among humans, who venerated him because he was 'yang', good, and was always ready to help them. One day, the God of Thunder, jealous of the offerings the men had brought to Yu, in a burst of anger, crushed the sky with his hatchet. So, the sky fell on Earth in seven pieces black like coal. Light disappeared taking with it all existing things.

At first Yu felt sad for the world, and then felt nostalgic. So he decided to collect the seven black pieces of the sky and, in memory of the former world, began to reassemble several kinds of shapes: animals, plants and human beings that had disappeared. But after finishing each shape, its shadow left it and wandered the deserted world crying about its misfortune. 

These complaints reached the ears of the God of Thunder who was touched and, to remedy the harm he had caused, he created from each shadow the body of a living being to repopulate the Earth. From that time on, our shadow faithfully follows every move we make and with the seven pieces of the sky, called Qi Qiao Ban (literally 'seven boards of cunning'), everything on Earth can still be shaped”.

Source: Almanacco del Matematico, © G. Sarcone, 2001

The game 

The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape (given only an outline or silhouette) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century.

Pieces 

Choose a unit of measurement so that the seven pieces can be assembled to form a square of side one unit and having area one square unit, the seven pieces are:

    * 2 large right triangles (see picture below: no. 1 and 2)
    * 1 medium right triangle (see picture below: no. 4)
    * 2 small right triangle (see picture below: no. 5 and 7)
    * 1 square (see picture below: no. 6)
    * 1 parallelogram (see picture below: no. 3)