Tangram

From Wikipedia, the free encyclopedia

A typical tangram construction
A typical tangram construction

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 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. The pieces are:

Contents

[edit] History

Wooden Tangram Set
Wooden Tangram Set

The tangram is very possibly originated from the yanjitu (燕几圖) furniture set 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.

Another legend states that a servant of a Chinese emperor was carrying a ceramic tile, extremely expensive and extremely fragile. The servant tripped, shattering the tile. In a panic, the servant desperately tried to reassemble the tile into a square, but could not. He did realize, however, that many other shapes could be formed from the pieces.

The tans are often stored as a rectangle
The tans are often stored as a rectangle

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.[citation needed]

The word "tangram" is built from TANG + 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 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.

Tradional 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.

[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

Tan construction
Tan construction

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.

Easy Tan construction
Easy Tan construction

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

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

[edit] External links

Wikimedia Commons has media related to:
Retrieved from "http://en.wikipedia.org../../../t/a/n/Tangram.html"