Tangram

Tangram comprises a square dissected into seven simple geometric shapes. The object of the game is to form other shapes from these seven pieces with predefined profiles – usually objects, animals and people, but also geometric shapes. All the pieces must be used in the process and they are not allowed to overlap.

History

The game is thought to have originated in China: the mathematics of the third century AD and later furniture design both feature the fragmentation of geometric shapes that is strongly reminiscent of Tangram shapes. The puzzle was first documented in its present form in China in the early nineteenth century before being introduced to the Occident a few years later. The name Tangram appears to have been coined in the mid-nineteenth century by Thomas Hill, a mathematician, game inventor and president of the Harvard University. Since the spread of the puzzle in the West, a large number of books with Tangram shapes have been published.     

Mathematics

Sometimes, simple dissection puzzles present complex mathematical problems. One such issue is to determine all the convex polygons that can be assembled with the seven Tangram pieces. A polygon is convex if a line connecting any two points within the polygon runs completely within the polygon. In 1942 two mathematicians from the National University of Chekiang (China) published an article on the topic, in which they demonstrated that there is a total of thirteen convex polygons. They proceeded from the fact that the five larger pieces consist of right-angled isosceles triangles which are congruent to the two smallest triangles. Moreover, they considered all the convex shapes that can be formed with sixteen such triangles and excluded those that cannot be constructed with Tangram pieces.