Tangram

Tangram is a dissection puzzle. It consists of seven pieces, called ''tans'', which fit together to form a shape of some sort. The objective is to form a specific shape with seven pieces. The shape has to contain all the pieces, which may not overlap.

History

The Tangram possibly originated from the ''yanjitu'' furniture set during the Song Dynasty. There is some variation to such furniture set during the Ming Dynasty, and later became a set of wooden blocks for playing.

According to other authors, the earliest known reference to tangram appears in a Chinese book dated 1813, which was probably written during the reign of the Jiaqing Emperor.


While the tangram is often said to be ancient, its existence in the Western world has been verified no earlier than 1800. Tangrams were brought to America by Chinese and American ships during the first part of the nineteenth century. The earliest example known is made of ivory in a silk box and was given to the son of an American ship owner in 1802.

The word "tangram" is built from + GRAM. The word "Tangram" was first used by Thomas Hill, later President of Harvard, in his book ''Geometrical Puzzle for the Youth'' in 1848.

The author and mathematician Lewis Carroll reputedly was a great enthusiast of tangrams and possessed a Chinese book with tissue-thin leaves containing 323 tangram designs. Napoleon was said to have owned a Tangram set and Chinese problem and solution books while he was imprisoned on the island of St. Helena although this has been contested by Ronald C. Read. Photos are shown in "The Tangram Book" by Jerry Slocum.

In 1903, Sam Loyd wrote a spoof of tangram history, ''The Eighth Book Of Tan'' convincing many people that the game was invented 4,000 years ago by a god named Tan. The book included 700 patterns some of which are not possible.

Traditional tangrams were made from stone, bone, clay or other easy to get materials. Nowadays they can be made from plastic, wood or other modern materials.

Mathematical proofs

Fu Tsiang Wang and Chuan-chin Hsiung proved in 1942 that there only existed 13 patterns .

Convex tangrams are very special and there are so few of them. Ronald C. Read in his book “Tangrams: 330 Puzzles” asked for any other special kinds of tangrams that would be more numerous than the convex ones, and yet not in number. He proposed to investigate the "snug tangrams" with the use of a computer.

An estimate of ten millions of configuration has been reported, focusing on the fully matched patterns , which are indeed a wider set than the Read's "snug tangram".

The pieces

Sizes are relative to the big square, which is defined as being of width, height and area equal to $\backslash scriptstyle$.
* 5
** 2 small
** 1 medium size
** 2 large size
* 1 square
* 1 parallelogram

Of these 7 pieces, the parallelogram is unique in that its mirror image cannot be obtained by rotation. Thus, it is the only piece that needs to be flipped when forming some silhouettes. Since there is only one such piece, every possible silhouette or its mirror image can be formed with a set of one-sided tangrams .