The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; lit. 'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern (given only an outline) generally found in a puzzle book using all seven pieces without overlap. Alternatively the tans can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline. It is reputed to have been invented in China sometime around the late 18th century and then carried over to America and Europe by trading ships shortly after.[1] It became very popular in Europe for a time, and then again during World War I. It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education. [2][3][4]
The origin of the English word 'tangram' is unclear. One conjecture holds that it is a compound of the Greek element '-gram' derived from γράμμα ('written character, letter, that which is drawn') with the 'tan-' element being variously conjectured to be Chinese t'an 'to extend' or Cantonese t'ang 'Chinese'.[5] Alternatively, the word may be derivative of the archaic English 'tangram' meaning "an odd, intricately contrived thing".[6]
Despite its relatively recent emergence in the West, there is a much older tradition of dissection amusements in China which likely played a role in its inspiration. In particular, the modular banquet tables of the Song dynasty bear an uncanny resemblance to the playing pieces of the tangram and there were books dedicated to arranging them together to form pleasing patterns.[9]
According to Western sources, however, the tangram's historical Chinese inventor is unknown except through the pen name Yang-cho-chu-shih (Dim-witted (?) recluse, recluse = 处士). It is believed that the puzzle was originally introduced in a book titled Ch'i chi'iao t'u, which was already reported as lost in 1815 by Shan-chiao in his book New Figures of the Tangram. Nevertheless, it is generally believed that the puzzle was invented about 20 years earlier.[10]
The prominent third-century mathematician Liu Hui made use of construction proofs in his works and some bear a striking resemblance to the subsequently developed banquet tables which in turn seem to anticipate the tangram. While there is no reason to suspect that tangrams were used in the proof of the Pythagorean theorem, as is sometimes reported, it is likely that this style of geometric reasoning went on to exert an influence on Chinese cultural life that lead directly to the puzzle.[11]
The puzzle eventually reached England, where it became very fashionable. The craze quickly spread to other European countries. This was mostly due to a pair of British tangram books, The Fashionable Chinese Puzzle, and the accompanying solution book, Key.[13] Soon, tangram sets were being exported in great number from China, made of various materials, from glass, to wood, to tortoise shell.[14]
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.[15] 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, Det nye chinesiske Gaadespil (The new Chinese Puzzle Game), consisted of 339 puzzles copied from The Eighth Book of Tan, as well as one original.[15]
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.[16]
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 alternative title for the "Anchor Puzzle" sets.[19][20]
A tangram paradox is a dissection fallacy: Two figures composed with the same set of pieces, one of which seems to be a proper subset of the other.[21] One famous paradox is that of the two monks, attributed to Henry Dudeney, which consists of two similar shapes, one with and the other missing a foot.[22] In reality, the area of the foot is compensated for in the second figure by a subtly larger body.
Over 6500 different tangram problems have been created from 19th century texts alone, and the current number is ever-growing.[26] Fu Traing Wang and Chuan-Chih Hsiung proved in 1942 that there are only thirteen convex tangram configurations (config 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).[27][28]
Dating back hundreds of years, tangram puzzles use seven shapes in various combinations to build pictures. These virtual tangrams offer tons of opportunities for kids to practice spatial rotation and explore the relationships between shapes. Our tangram virtual manipulative was developed using physics to allow for the feel of concrete pieces, as they can be rotated, moved around, and bumped into each other. More than ten different puzzles are included; see if you can solve them all!
Choose from all sorts of different tangram shapes, or play in free mode and make your own tangram masterpiece! Drag the different coloured shapes to their place in the design, and rotate them if you need to. Save a photo of your finished tangram to your desktop to share.
Hi @Jorge this is such a fun concept. You can use the shapes within the app to create some of these tangram shapes. To rotate shapes, you can use the "handles" at the side of each shape. I'll share a video with you for more info.
Ooh, smart! I used to love playing with tangrams when I was younger, but I never had any magnetic ones. I might make some of these even though my daughter is way too young for them.
You could use an acrylic sealer on top of the mod podge to reduce the stickiness if you can't find the gel medium.
Thankyou! I made some and they're great. I did it slightly differently to your tutorial, and they turned out like this: -little-crafty.blogspot.com.au/2012/08/magnetic-tangrams.html. They're too big for a tin, so I'll have to think of something else ?
Some people (hi, Sweetie) are not fond of tangrams, and some people (hi, Bubbe) could sit and fiddle with tangrams all damn day and never come up for air. I might be one of the latter type. I started writing a book of Jewish Tangrams, got stymied with the vector software, and then got distracted by my Naturalist studies. But I still hold that tangrams are neato, hands-on, mind-enlarging tools, and oh-so versatile.
My favorite tangram materials are thick wood and the foam-covered magnets, my least favorite are paper or thin plastic. Tangrams need sensorial heft to be truly fun, and a bit of weight makes it a pleasure just to scoot the tans around. Toast works, for a laugh and a nibble, and for a thematic nod to Hanukkah.
Our gel tangrams are better than ever! Soft and squishy, the glittery gel-filled tangram shapes keep both fingers and minds busy. Squeeze the seven colorful shapes as you solve tangram puzzles found on our Tangram Cards. Can you use all seven pieces to form a square? Can you make a house or boat? Be creative! There are thousands of pictures you can create on your own. Terrific tool for enhancing focus, attention and fine motor coordination.
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