Tangram

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Tangram (Chinese: 七巧板; pinyin: qī qiǎo bǎn; literally "seven boards of cunning") 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:

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>)

1 History
2 Obtaining a set of tans
- 2.1 Make your own
- 2.2 Buy a set
3 See also
4 Further reading
5 External links

[edit] History

Image:Tangram rectangle.svg

While the tangram is often said to be ancient, its existence 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.^{[citation needed]}

The word "tangram" has no meaning in Chinese, the English word is built from TANG + GRAM. In the Cantonese dialect, T'ang (唐) 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.^{[citation needed]}

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!

[edit] Obtaining a set of tans

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

[edit] 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.

Image:Make1.jpg

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!

[edit] Buy a set

Image:Tangram-set-blueplas.jpg

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 manipulatives.

[edit] See also

[edit] Further reading

2nd Scientific American Book of Mathematical Puzzles and Diversions, Martin Gardner, Simon & Schuster, 1961
"A Heuristic Solution to the Tangram Puzzle", E. S. Deutsch & K. C. Hayes Jr., Machine Intelligence v7, p205-240, 1972
A Sage's Journey, The Story of Tangrams, John L. Lehet, Mathmaverick Press, 1998
A Teacher's Guide to Tangram Mastery, Allan F. Hirsch, Alleyoop Enterprises, 1996
"A Theorem on Tangram", F. T. Wang & C. C. Hsiung, American Mathematical Monthly v49, 1942
Adventure of the Beautiful Princess in Triangle Land, F. Gregory Hartswick, Siman & Schuster Publishers, 1925
Amusements in Mathematics, H. E. Dudeney, Dover Publications, 1958
Anno's Math Games, Mitsumasa Anno, Philomel Books
Creative Puzzles of the World, Pieter Van Delft & Jack Botermans, Harry N. Abrams, Inc., 1978
Ess Tangram Cards; The Elementary Science Study, Dale Seymour Publications, Addison Wesley Publishing Company. Three sets: Grades K-8, Set II, Set III
Geometry and Fractions with Tangrams, Barbara Bando Irvin
Granfather 'Tang's Story, Ann Tompert, Crown Publisher, Inc., 1990
"Mathematical Games-on the Fanciful History and the Creative Challenges of the Puzzle Game of Tangrams", Martin Gardner, Scientific American, p98-103, Aug. 1974
"More on Tangrams", Martin Gardner, Scientific American, p187-191, Sep. 1974
Puzzles of Old and New, Jerry Slocum & Jack Botermans, 1986
Pythagoras-A Game of 179 Puzzles, Kohner Bros. Inc. (179 shapes)
Sam Loyd's Book of Tangram Puzzles (The 8th Book of Tan Part I), Sam Loyd, Dover Publications, 1968
Tangram ABC Kit, Susan Johnston, Dover Publications
Tangram Box, James Lyon, Book-in-a-Box Publications, 2005
THE TANGRAM ABC BOOK, DR. T. E. FOSTER, BOOKSURGE, 2006, ISBN 1-4196-4915-9
TANGRAM PATTERNS, THOMAS E. FOSTER, Creative Publications Inc., 1977, ISBN 0-88488-081-8
THEN AND NOW ON OLD MACDONALD'S FARM, A TANGRAM NUMBER BOOK, DR. T. E. FOSTER, BOOKSURGE, 2006, ISBN 1-4196-4916-7
Tangram Puzzle Game Binary Arts ISBN 0-641-50914-6
Tangram Puzzles: 500 Tricky Shapes to Confound & Astound / Includes Deluxe Wood Tangrams Chris Crawford ISBN 0-8069-7589-X, 2002 Sterling Publishing Company (500 shapes)
Tangram, The Ancient Chinese Shapes Game, Joost Elfers, Penguin Books, 1976 ISBN 0-14-004181-8
Tangramath, Dale Seymour, Creative Publications Inc., 1971
Tangrams, 330 Puzzles, Ronald C. Read, Dover Publications, 1965 ISBN 0-486-21483-4 (330 shapes)
"Tangrams", Harry Lindgren, Journal of Recreational Mathematics, p184-192, 1969
Tangrams, I Ching Games of Duke Tan of Chou and C. C. T'ung, H. Y. Li, Cadleon Press, 1971
Tangrams, Picture Making Puzzle Game, Peter Van Note, Tuttle
Tangrams: 1,600 Ancient Chinese Puzzles, Joost Elffers, Michael Schuyt Barnes & Noble Books, September 2001 ISBN 0-7607-2712-0 (1,600 shapes) box with pieces
The Book of Ingenious and Diabolic Puzzles, Jerry Slocum & Jack Botermans, Random House Inc., 1994
The Fun with Tangram Kit, Susan Johnston, Dover Publications ISBN 0-486-23436-3
The Master Revealed-A Journey with Tangrams, Barbara E. Ford, Tandoras's Box Press, 1990 ISBN 0-9627337-8-4 [1]
Tangrams - The Magnificent Seven Piece Puzzle, Barbara E. Ford, Tandoras's Box Press, 2003
The Super Source-Tangrams, Dale Seymour
The Tangram Book, Jerry Slocum, Dieter Gebhardt, Jack Botermans, Monica Ma, Xiaohe Ma 2003 ISBN 1-4027-0413-5 Sterling Publishing Company (Comprehensive, illustrated history, 1,756 problem figures) beautiful photos of historic Tangrams from Asia, Europe and America, coffee table book
World of Games, Their Origin and History, Jack Botermans, 1981