Tangram

Brief History of Tangrams

The tangram is one of the historical disection puzzles originating from imperial China.  Various tangram patterns may be form from the simple geometric pieces of the tangram puzzle.  One documentation on tangrams was recorded in a Chinese book dated 1813, however, tangrams have been know to have existed much earlier in history.  Another book, "New Figures of the Tangram" by Shan-Chiao, was published in China in 1815, which contained 374 tangram patterns.  These documentations were written during the reign of emperor Chia-Ching, during the time when tangrams were at the summit of its popularity in China.  Tangrams were called 七巧板 or "Chi-Chiao Pan", meaning "the seven intriguing pieces".  Known to the Chinese as the "wisdom puzzle", tangrams have been well-known to the western world since the 19th century.  Well-known people, such as Edgar Allan Poe, Napoleon, H.E.Dudeney, and Sam Loyd have all shown great interest in tangrams.  By 1817, tangrams had gain popularity in Europe and America.  In fact, the word tangram officially appeared in Webster's dictionary in 1864.

The Tangram Puzzle Set

The tangram puzzle set is composed of seven pieces.  One of the piece is a square, another piece is a rhomboid, and the other five pieces are isosceles right triangles of various sizes.  Of these triangular pieces, two are small size triangles, one is a medium sized triangle and and two are large size  triangle.  The area of a large size triangle is twice the area of the medium size triangle.  The area of the medium size triangle is twice the area of an small size triangle. The area of the square is also twice the area of an small size triangle.  The area of the rhomboid is the same as that of the square.  All the angles in these pieces are either 45, 90 or 135 degrees.  Making a tangram set from a piece of square board is easy.

Playing Tangrams

The instructions for playing tangrams are simple and very easy to understand.  The objective of the puzzle is to form a figure using the tangram pieces.  People find this seven-piece tangram puzzle fascinating and delightful because there are a large variety of ways of putting these pieces together.  Using one's own creativity, various tangram figures may be formed.  In fact, thousands and thousands of designs have been created over the years by just rearranging these seven tangram pieces. 

Other interesting facts about Tangrams

The tangram pieces may be rearrange into various figures and designs. These designs not only include simple geometric shapes shown below, but also shapes of different animals, such as birds, dogs, and cat.  The designs also include numerous other shapes of popular objects.

As can be easily noted, various simple polygonal shapes may be formed from seven basic pieces.  Some of the simple polygonal shapes resulting from rearraging tangram pieces include the following:

Perhaps, the Chinese had in their observations that the seven basic tangram pieces were the basis of the formation of various simple polygons, and therefore can be used to form numerous other shapes and extraordinary images.

Also to be noted is that the shapes of each of the seven tangram pieces may be formed from the seven tangram pieces, although resulting in a larger size version.  This means that each of the seven tangram pieces may further be subdivided into a set of the seven smaller tangram pieces.

One of the popular books on Tangrams is the "Eighth Book of Tan" by Sam Loyd, an american puzzle expert.  This book contains around 700 tangram patterns.  Lyod called this the "eight" book because he claimed that about four thousand years ago, a Chinese name Tan had compiled seven books on Tangrams.

Convex Tangram Shapes

The polygon patterns from tangrams shown above are convex shape patterns.  In a convex shape, such as those shown above, a line segment drawn from any point on the edge or within the shape to another point on the edge or within the shape will always be

within the shape.  In 1942, mathematicians proved that there are only 13 possible convex tangram patterns.  Six of there were shown above.

Next:   Making Your Own Tangram Set

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Bridge SwanFish Letter EHexagon HorsemanKangaroo GlassDuck PipeBowl CamelHelicopter CrowSquirrel GooseHare Running ManHouse CatBoating Man Sitting PersonShirt CandlestickChristmas Tree Wine GlassArrow RabbitDancer Mountain RangeLetter C SailboatGateway Double ArrowSpace Capsule ChairRooster Ferry

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TangramFrom Wikipedia, the free encyclopedia

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For other uses, see Tangram (disambiguation).

The tangram (Chinese: 七巧板; pinyin: qī qiǎo bǎn; literally "seven boards of skill") is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape (given only an outline or silhouette) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century. It became very popular in Europe for a time then, and then again during World War I. It is one of the most popular dissection puzzles in the world.[1][2]

History

Reaching the Western world (1815–1820s)

A caricature published in France in 1818, when the Tangram craze was at its peak. The caption reads: " 'Take care of yourself, you're not made of steel. The fire has almost gone out and it is winter.' 'It kept me busy all night. Excuse me, I will explain it to you. You play this game, which is said to hail from China. And I tell you that what Paris needs right now is to welcome that which comes from far away.' "

The tangram had already been around in China for a long time when it was first brought to America by Captain M. Donnaldson, on his ship, Trader, in 1815. When it docked in Canton, the captain was given a pair of Sang-hsia-k'o's Tangram books from 1815.[3] They were then brought with the ship to Philadelphia, where it docked in February 1816. The first Tangram book to be published in America was based on the pair brought by Donnaldson.

The puzzle was originally popularized by The Eighth Book Of Tan, a fictitious history of Tangram, which claimed that the game was invented 4,000 years prior by a god named Tan. The book included 700 shapes, some of which are impossible to solve.[4]

Cover art from "The 8th Book of Tan", by Sam Loyd, a spoof of the puzzle's history that began the Tangram Craze in the Western World

The puzzle eventually reached England, where it became very fashionable indeed.[3] The craze quickly spread to other European countries.[3] This was mostly due to a pair of British Tangram books, The Fashionable Chinese Puzzle, and the accompanying solution book, Key.[5] Soon, tangram sets were being exported in great number from China, made of various materials, from glass, to wood, to tortoise shell.[6]

Many of these unusual and exquisite tangram sets made their way to Denmark. Danish interest in tangrams skyrocketed around 1818, when two books on the puzzle were published, to much enthusiasm.[7] The first of these was Mandarinen (About the Chinese Game). This was written by a student at Copenhagen University, which was a non-fictional work about the history and popularity of tangrams. The second, Der nye chinesisre Saadespil (The new Chinese Puzzle Game), consisted of 339 puzzles copied from The 8th Book of Tan, as well as one original.[7]

One contributing factor in the popularity of the game in Europe was that although the Catholic Church forbade many forms of recreation on the sabbath, they made no objection to puzzle games such as the tangram.[8]

The second craze in Germany and America (1891–1920s)

Tangrams were first introduced to the German public by industrialist Friedrich Adolf Richter around 1891.[9] The sets were made out of stone or false earthenware,[10] and marketed under the name "The Anchor Puzzle".[9]

More internationally, the First World War saw a great resurgence of interest in Tangrams, on the homefront and trenches of both sides. During this time, it occasionally went under the name of "The Sphinx", an alternate title for the "Anchor Puzzle" sets.[11][12]

Paradoxes

Loyd's paradox

A tangram paradox is an apparent dissection fallacy: Two figures composed with the same set of pieces, one of which seems to be a proper subset of the other.[13] One famous paradox is that of the two monks, attributed to Dudeney, which consists of two similar shapes, one with and the other missing a foot.[14] Another is proposed by Sam Loyd in The Eighth Book Of Tan:

The seventh and eighth figures represent the mysterious square, built with seven pieces: then with a corner clipped off, and still the same seven pieces employed.[15]

Other similar, but possible, apparent paradoxes are in fact fallacious. For example, in the case of the two monks mentioned above, the foot is actually compensated for in the second figure by a subtly larger body.[13]

Number of configurations

The 13 convex shapes matched with Tangram set

Over 6500 different tangram problems have been compiled from 19th century texts alone, and the current number is ever-growing.[16] The number is finite, however. Fu Traing Wang and Chuan-Chin Hsiung proved in 1942 that there are only thirteen convex tangram configurations (configurations such that a line segment drawn between any two points on the configuration's

edge always pass through the configuration's interior, i.e., configurations with no recesses in the outline).[17][18]

PiecesChoosing a unit of measurement so that the seven pieces can be assembled to form a square of side one unit and having area one square unit, the seven pieces are:

2 large right triangles (hypotenuse , sides , area ) 1 medium right triangle (hypotenuse , sides , area )

2 small right triangle (hypotenuse , sides , area )

1 square (sides , area )

1 parallelogram (sides of and , area )

Of these seven pieces, the parallelogram is unique in that it has no reflection symmetry but only rotational symmetry, and so its mirror image can only be obtained by flipping it over. Thus, it is the only piece that may need to be flipped when forming certain shapes.

See also Tiling puzzle Ostomachion

Mathematical puzzle

References1. ̂ Slocum, Jerry (2001). The Tao of Tangram. Barnes & Noble. p. 9. ISBN 978-1-4351-

0156-2.2. ̂ Forbrush, William Byron (1914). Manual of Play. Jacobs. p. 315.

http://books.google.com/?id=FpoWAAAAIAAJ&pg=PA315&dq=%22The+Anchor+Puzzle%22#v=onepage&q=%22The%20Anchor%20Puzzle%22&f=false. Retrieved 10/13/10.

3. ^ a b c Slocum, Jerry (2003). The Tangram Book. Sterling. p. 30. ISBN 049725504134.

4. ̂ Costello, Matthew J. (1996). The Greatest Puzzles of All Time. New York: Dover Publications. ISBN 0-486-29225-8.

5. ̂ Slocum, Jerry (2003). The Tangram Book. Sterling. p. 31. ISBN 049725504134.

6. ̂ Slocum, Jerry (2003). The Tangram Book. Sterling. p. 49. ISBN 049725504134.

7. ^ a b Slocum, Jerry (2003). The Tangram Book. Sterling. pp. 99–100. ISBN 049725504134.

8. ̂ Slocum, Jerry (2003). The Tangram Book. Sterling. p. 51. ISBN 049725504134.

9. ^ a b http://www.archimedes-lab.org/tangramagicus/pagetang1.html

10. ̂ Treasury Decisions Under customs and other laws, Volume 25. United States Department Of The Treasury. 1890–1926. p. 1421. http://books.google.com/?id=MeUWAQAAIAAJ&pg=PA1421&lpg=PA1421&dq=%22The+Anchor+Puzzle%22#v=onepage&q=%22The%20Anchor%20Puzzle%22&f=false. Retrieved 9/16/10.

11. ̂ Wyatt (26 April 2006). "Tangram – The Chinese Puzzle". BBC. http://www.bbc.co.uk/dna/h2g2/alabaster/A10423595. Retrieved 3 October 2010.

12. ̂ Braman, Arlette (2002). Kids Around The World Play!. John Wiley and Sons. p. 10. ISBN 9780471409847. http://books.google.com/?id=fNnoxIfJg5UC&printsec=frontcover&dq=Kids+Around+The+World+Play!&q. Retrieved 9/5/2010.

13. ^ a b Tangram Paradox, by Barile, Margherita, From MathWorld – A Wolfram Web Resource, created by Eric W. Weisstein.

14. ̂ Dudeney, H. (1958). Amusements in Mathematics. New York: Dover Publications.

15. ̂ Loyd, Sam (1968). The eighth book of Tan – 700 Tangrams by Sam Loyd with an introduction and solutions by Peter Van Note. New York: Dover Publications. p. 25.

16. ̂ Slocum, Jerry (2001). The Tao of Tangram. Barnes & Noble. p. 37. ISBN 978-1-4351-0156-2.

17. ̂ Fu Traing Wang; Chuan-Chih Hsiung (November 1942). "A Theorem on the Tangram". The American Mathematical Monthly 49 (9): 596–599. doi:10.2307/2303340. JSTOR 2303340.

18. ̂ Read, Ronald C. (1965). Tangrams : 330 Puzzles. New York: Dover Publications. p. 53. ISBN 0-486-21483-4.

Further reading Anno, Mitsumasa. Anno's Math Games (three volumes). New York: Philomel Books, 1987. ISBN

0399211519 (v. 1), ISBN 0698116720 (v. 2), ISBN 039922274X (v. 3). Botermans, Jack, et al. The World of Games: Their Origins and History, How to Play Them, and

How to Make Them (translation of Wereld vol spelletjes). New York: Facts on File, 1989. ISBN 0816021848.

Dudeney, H. E. Amusements in Mathematics. New York: Dover Publications, 1958.

Gardner, Martin . "Mathematical Games—on the Fanciful History and the Creative Challenges of the Puzzle Game of Tangrams", Scientific American Aug. 1974, p. 98–103.

Gardner, Martin. "More on Tangrams", Scientific American Sep. 1974, p. 187–191.

Gardner, Martin. The 2nd Scientific American Book of Mathematical Puzzles and Diversions. New York: Simon & Schuster, 1961. ISBN 0671245597.

Loyd, Sam. Sam Loyd's Book of Tangram Puzzles (The 8th Book of Tan Part I). Mineola, New York: Dover Publications, 1968.

Slocum, Jerry, et al. Puzzles of Old and New: How to Make and Solve Them. De Meern, Netherlands: Plenary Publications International (Europe); Amsterdam, Netherlands: ADM International; Seattle: Distributed by University of Washington Press, 1986. ISBN 0295963506.

Slocum, Jerry, et al. The Tangram Book: The Story of the Chinese Puzzle with Over 2000 Puzzles to Solve. New York: Sterling Publishing Company, 2003. ISBN 1-4027-0413-5.

External links

Wikimedia Commons has media related to: Tangrams

"Tangram" by Enrique Zeleny, Wolfram Demonstrations Project "New Tangram paradoxes" by Gianni A. Sarcone, Archimedes Laboratory Project

Retrieved from "http://en.wikipedia.org/wiki/Tangram"

Tangram

Tangram adalah permainan puzzle tertua yang tercatat dalam sejarah. Tangram berasal dari China.Menurut salah satu cerita. Ada seorang tukang keramik yang diperintah oleh Kaisar untuk membuat motif lantai istana kaisar. Karena pusing menentukan motif yang cocok, akhirnya dia membuat tangram tersebut. Dari tangram dia bisa membuat berbagai macam motif. Gambar di bawah memperlihatkan sebagian dari berbagai macam motif tersebut.

Ada banyak cerita tentang tangram. Sejarah pastinya tidak ada yang tahu. Tangram pertama kali tercatat pada literatur di China pada tahun 1813 [1]. Pembaca bisa search di internet dengan keyword “tangram”, akan keluar banyak gambar atau cerita tentang tangram.

Ada juga orang yang mencari berapa banyak bentuk convex (cembung) yang bisa dibentuk dari keping-keping tangram tersebut. Proof by Fu Traing Wang dan Chuan-Chih Hsiung [2] membuktikan bahwa

jawabannya adalah 13 (tiga belas). "Bentuk convex itu digambarkan sebagai berikut: bila ada suatu gambar di kertas dan Anda menggambar dua titik di dalam gambar tersebut ( lokasi titik boleh di mana saja, asal masih di dalam gambar ), lalu menarik garis lurus antara dua titik tersebut, jika ternyata garis tersebut selalu berada di dalam gambar, maka gambar tersebut adalah convex. Gambar di bawah memperlihatkan bentuk convex yang dapat disusun oleh keping-keping tangram. Jika Anda dapat mencari bentuk ke-14, Anda mungkin bisa tercatat dalam sejarah.

Tangram adalah permainan puzzle yang sangat menyenangkan. Tidak hanya menyenangkan tapi juga melatih imajinasi. Menarik bukan? Karena dari tujuh keping tangram, bisa dibuat bermacam-macam bentuk. Tanpa perlu penjelasan lebih dalam, dengan melihat contoh-contoh gambar di atas, sudah cukup jelas bagi pembaca bahwa tangram bisa melatih imajinasi.

Ini menyebabkan tangram cocok dipakai untuk pendidikan anak usia dini. Gambar di bawah memperlihatkan, tangram digunakan pada sebuah TK di Amerika Serikat [3].

Ada paradoks di tangram. Coba lihat gambar di bawah.

Siluet dua orang, sama-sama dibuat dari tujuh keping tangram. Satu berkaki, yang satu lagi tidak. Apakah pembaca bisa membuat siluet dua orang tersebut? Bagaimana dengan kakinya? Ke mana perginya kaki pada siluet tak berkaki? Paradoks pada tangram ditemukan oleh Henry Ernest Dudeney

(10 April 1857–24 April 1930, English author and mathematician), disebut Paradoks Dudeney (Dudeney’s Paradox).

Apakah imajinasi Anda sudah cukup baik? Untuk latihan, Anda bisa mencoba menyusun gambar-gambar di bawah ini. Tentunya dengan tangram kami yang tersedia dalam 2 pilihan: dari kayu dan kain.....Selamat mencoba.....

Referensi:[1] http://en.wikipedia.org/wiki/Tangram[2] http://www.mathematische-basteleien.de/tangrams.htm

[3] http://kindergarten2.homestead.com/Thanksgiving.html    [4] Berbagai sumber lain dari internet