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 Tangram is a Chinese puzzle, and a type of dissection puzzle. A
tangram consists of 7 pieces, called tans, which fit together to form a square.
The objective is to form a specific shape with seven pieces. The shape has to
contain all the pieces, which may not overlap. The pieces are:
History
The tangram is very possibly originated from the "Yanji furniture" during the
Song Dynasty. According to historical Chinese records, the furniture set was
originally a set of 6 rectangular tables. Later, an additional triangular table
was added to the set, and people can arrange the 7 tables into a big square
table. There is some variation to such furniture set during the Ming Dynasty,
and later became a set of wooden blocks for playing.
While the tangram is often said to be ancient, its existence in the Western
world has only been verified as far back as 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" has no meaning in Chinese, the English word is built from
TANG + GRAM. In the Cantonese dialect, T'ang is a synonym of "Chinese". The word
"Tangram" was first used by Thomas Hill, later President of Harvard, in his
book, "Geometrical Puzzle for the Youth" in 1848.
The puzzler Laura Lissi devised many tangram puzzles.
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 owned a Tangram set and Chinese problem and solution
books while he was imprisoned on the island of St. Helena. Photos are shown in
"The Tangram Book" by Jerry Slocum.
Obtaining a Set of Tans
Many tangram enthusiasts get started with a gift set. Others can make or buy a
set of tans.
 Make Your Own
A set of tans can be constructed with compass and straightedge. Nearly any thin,
stiff material, such as cardboard or foam board, can be worked with the
appropriate cutting tool. If working wood or metal with a saw, a thin blade
should be chosen to minimize kerfs error and ensure the pieces fit properly.
Edges may be sanded smooth and the tans painted any color.
Construction (see diagram): Starting with a square, draw the line segment bh.
The point d bisects bh, and c and f in turn bisect bd and dh, respectively.
Segment ei forms the medium sized triangle on the bottom right. It connects the
bisectors, or midpoints, of the bottom and right sides of the square. Now, draw
lines from a to g (the midpoint of ei), from c to g, and from f to i. Once the
figure has been drawn, cut along the lines to make the set of seven tans.
 Another way to draw the cut lines for a tangram set is as follows.
Use a square the size you want the finished puzzle to be. It can be a square of
the material you would like your set to be made of or, if more convenient, a
paper template to transfer the design.
Draw a four by four grid on the material as shown in the picture. This will
scale up or down for any size square, the four squares by four squares part is
the important thing here. You then mark off the blue lines as shown. Cut your
material carefully along these blue lines. This will produce the seven tan
pieces; five triangles, one square and one parallelogram. As noted above,
slicing rather than sawing will produce the best result. Enjoy!
Buy a Set
Tangram sets are widely available in a wide range of materials and prices, with
or without corresponding puzzle books. Teacher supply stores offer inexpensive
sets, usually sold as mathematical manipulative.
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