[x] Close ad

TANGRAM

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:

Contents

History

While the tangram is often said to be ancient, its existence has only been verified as far back as 1800. Tangram 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 shipowner in 1802.

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". 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 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 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 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.

Buy a set

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.


See also

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
  • Tangram Patterns, Thomas Foster, Creative Publications Inc., 1977
  • Tangram Puzzle Game Binary Arts ISBN 0641509146
  • Tangram Puzzles: 500 Tricky Shapes to Confound & Astound / Includes Deluxe Wood Tangrams Chris Crawford ISBN 080697589X 2002 Sterling Publishing Company (500 shapes)
  • Tangram, The Ancient Chinese Shapes Game, Joost Elfers, Penguin Books, 1976 ISBN 0140041818
  • Tangramath, Dale Seymour, Creative Publications Inc., 1971
  • Tangrams, 330 Puzzles, Ronald C. Read, Dover Publications, 1965 ISBN 0486214834 (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 0760727120 (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 0486234363
  • The Master Revealed-A Journey with Tangrams, Barbara E. Ford, Tandoras's Box Press, 1990 ISBN 0962733784 [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 1402704135 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

External links