## Tangram

Tangram is a Chinese puzzle. The object, usually, is to take the seven pieces shown at the left (the smaller triangle which touches the center of the figure has the same height as the parallelogram below it), and arrange them to form a picture, such as that of the running figure also on the left (My solution is shown below). Books of Tangrams usually have a few hundred figures like this, for you to try to duplicate.

Apparently master puzzle maker Sam Loyd (in his Eighth Book of Tan) made up a fake history of the Tangram. He said that the puzzle was over 4000 years old, invented by Tan, a legendary author of the Seven Books of Tan. However, the puzzle seems to have originated about the year 1800. It is indeed of Chinese origin, although the name "Tangram" is apparently half Chinese and half Western. There are similar puzzles, made from somewhat different disections of the square. Some are earlier than the Tangram.

One minor puzzle is how to arrange the seven pieces to form two squares of equal area. The solution to this, and to the running figure, are shown below.

On the left are two famous tangram chinamen. Some people find it surprising that two such similar figures can be made with the same tangram pieces. The solutions to these are also shown below.

Here is one of Sam Loyd's pictures. Like the runner above, this is a surprisingly subtle and expressive work of art.

Solutions:

These "puzzles" are generally not difficult to solve. By carefully examining the solid colored figure, you should be able to tell exactly which pieces go where. To the left is one of the two squares. The other square is made up of the two large triangles. Also we see my solution for the running figure.

On the right are the two Chinamen. The bottom two pieces are the only differences. Actually, I see that we need to use the medium sized triangle as the hat.

Here is the female figure.

Tangrams may be more challenging and interesting, if you try to create your own pictures.