Tangram

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Image:Tangram-man.png Tangram (Template:Zh-cpl) is a Chinese puzzle. While the tangram is often said to be ancient, its existence has only been verified as far back as 1800.

It is said that the Pythagorean theorem was discovered in the Orient with help of tangram pieces. Jacob Bronowski on his television series The Ascent of Man demonstrated a method of proving the Theorem using pieces similar to those of the tangram, saying that the Pythagoreans may have used this method.

The word "tangram" has no meaning in Chinese; the English word is built from TANG + GRAM. In the Cantonese dialect, Tang (唐) is a synonym of "Chinese".

A tangram consists of 7 pieces, called tans, which fit together to form a square. The pieces are:

5 right isosceles triangles
- 2 small (legs of 1)
- 1 medium size (legs of <math>\sqrt{2}</math>)
- 2 large size (legs of 2)
1 square (side of 1)
1 parallelogram (sides of 1 and <math>\sqrt{2}</math>)

The objective is to form a specific shape with seven pieces. The shape has to contain all the pieces, which may not overlap.

Image:Tangram rectangle.png The puzzler Sam Loyd 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 allegedly passed his time working with tangrams in Elba.

Tangram is said to have been brought to America by Western sailors who stopped in China during the opium trade, however there is no evidence to support this claim.

1 Obtaining a set of tans
- 1.1 Make your own
- 1.2 Buy a set
2 See also
3 Further reading
4 External links

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Obtaining a set of tans

Many tangram enthusasts get started with a gift set. Others can make or buy a set of tans.

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Make your own

Image:Make a tangram.svg

A set of tans can be constructed with compass and straightedge. Nearly any thin, stiff material, such as cardboard or foamboard, can be worked with the appropriate cutting tool. If working wood or metal with a saw, a thin blade should be chosen to minimize kerf 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.

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Buy a set

Image:Tangram-set-blueplas.jpg

Tangram sets are available in a wide range of materials and prices, with or without corresponding puzzle books. Teacher supply stores offer inexpensive sets, usually sold as math manipulatives.

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