![\"\"](\"https:\/\/world.edu\/wp-content\/uploads\/2022\/12\/cute-boy-plays-tangram.jpg\")
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Have you played the puzzle game Tangram?<\/p>\n
I remember, as a child, being fascinated by how just seven simple wooden triangles and other shapes could offer endless entertainment. Unlike LEGO, the Tangram pieces do not snap together, and unlike the pieces of a jigsaw puzzle, they do not form a painted picture.<\/p>\n
Instead, Tangram invites you to fit all the pieces together to form countless varieties of shapes. You can make your own shapes or you can try to form shapes that others have created. For instance, here\u2019s one way to form a swan shape using Tangram pieces:<\/p>\n
![\"\"](\"https:\/\/world.edu\/wp-content\/uploads\/2022\/12\/Tangram.jpg\")
This is one of several ways to make a swan shape using Tangram. Can you find another? Shutterstock<\/p><\/div>\n
But it\u2019s not the only way to make a swan. Can you find others? If you do not have the physical puzzle at hand, you can\u00a0use<\/a>\u00a0a virtual version of Tangram.<\/p>\n Tangram is accessible and yet challenging, and an excellent\u00a0educational tool<\/a>. It\u2019s still\u00a0used<\/a>\u00a0in\u00a0schools<\/a>\u00a0today to help illustrate mathematical concepts and develop mathematical thinking skills. It even features a paradox or two.<\/p>\n Tangram is one of many rearrangement puzzles that have appeared throughout the ages. The earliest known rearrangement puzzle, the\u00a0Stomachion<\/a>, was invented by Greek mathematician Archimedes 2,200 years ago and was popular for centuries among Greeks and Romans.<\/p>\n It consists of 14 puzzle pieces that can fit together in the form of many different shapes. There are\u00a0536 different ways<\/a>\u00a0to fit the pieces together as a square.<\/p>\n Then there\u2019s the\u00a0Eternity Puzzle<\/a>, released in 1999, which consists of 209 blue puzzle pieces that together form a big circle-like shape. It was very popular and sold\u00a0500,000 copies<\/a>\u00a0worldwide, perhaps due to the 1 million British pounds promised to whoever first solved it.<\/p>\n Less than a year later, the mathematicians Alex Selby and Oliver Riordan\u00a0solved the puzzle<\/a>\u00a0and claimed the prize. The creator of the puzzle, the\u00a0controversial<\/a>\u00a0Christopher Monckton, said at the time he had to\u00a0sell his house<\/a>\u00a0to raise the prize money.<\/p>\n The origins of Tangram stretch back to the third century Chinese mathematician\u00a0Liu Hui<\/a>. Among many other\u00a0accomplishments<\/a>, Liu Hui used rearrangements of geometrical shapes to elegantly explain mathematical facts such as the\u00a0Gougu Rule<\/a>, also known as Pythagoras\u2019 Theorem.<\/p>\n Shapes can be rearranged to explain the Gougu Rule, also known as Pythagoras\u2019 Theorem. Animation by William B. Faulk, CC BY-SA 4.0, via Wikimedia Commons, CC BY<\/p><\/div>\n This rearrangement approach to geometry was later evident in the creation of 12th century\u00a0Chinese banquet tables<\/a>\u00a0(rectangular tables designed to be arranged into patterns that might please or entertain dinner guests).<\/p>\n A different version, known as a\u00a0butterfly table<\/a>, was popularised in the early 17th century and featured a broader variety of shapes. A surviving table set can be seen in the\u00a0Lingering Garden (Liu Yuan)<\/a>\u00a0which is part of a\u00a0UNESCO World Cultural Heritage<\/a>\u00a0site in Suzhou.<\/p>\n The Tangram was popularised as a puzzle game around the year 1800. Shutterstock<\/p><\/div>\n According to\u00a0The Tangram Book<\/a>\u00a0by Jerry Slocum and other authors, the Tangram was popularised as a puzzle game around the year 1800.<\/p>\n They report the inventor, an unknown Chinese person using the pen name Yang-Cho-Chu-Shih (\u201cDimwitted recluse\u201d), published Ch’i chi’iao t’u (\u201cPictures Using Seven Clever Pieces\u201d), a book containing hundreds of Tangram puzzle shapes.<\/p>\n This sparked a craze for the game in China. Other Tangram puzzle books were soon published, with some eventually making their way to Japan, the United States and England, where they were translated and extended.<\/p>\n During 1817-18, the Tangram\u00a0craze<\/a>\u00a0spread like\u00a0wildfire<\/a>\u00a0to France, Denmark and other European countries. Worldwide interest in Tangram has endured ever since.<\/p>\n The lasting popularity of Tangram might partly be due to it allowing so many shapes with so few pieces.<\/p>\n Researchers have found that Tangram can help students\u2019\u00a0visual and geometric thinking<\/a>\u00a0and even their\u00a0arithmetic skills<\/a>.<\/p>\n Tangram may help in the assessment of children\u2019s learning of\u00a0written languages<\/a>\u00a0and of their\u00a0emotional regulation skills<\/a>.<\/p>\n For most people, though, Tangram is just a fun and creative challenge.<\/p>\n There are also some Tangram \u201cparadox\u201d puzzles discussed in\u00a0The Tangram Book<\/a>\u00a0and elsewhere online, where Tangram pieces are arranged to make two seeming identical shapes (but where one appears to have a leftover piece).<\/p>\n The two monks Tangram paradox. AlphaZeta, CC0, via Wikimedia Commons, CC BY<\/p><\/div>\n Can you explain the \u201cparadox\u201d \u2013 why one has a triangular \u201cfoot\u201d and the other does not, even though both images use all seven pieces?<\/p>\n As a bonus challenge, perhaps you can you solve the similar infinite chocolate bar \u201cparadox\u201d popularised on Instagram and TikTok.<\/p>\nA long history of rearrangement puzzles<\/strong><\/h4>\n
![\"\"](\"https:\/\/world.edu\/wp-content\/uploads\/2022\/12\/GouguRule.jpg\")
![\"\"](\"https:\/\/world.edu\/wp-content\/uploads\/2022\/12\/Tangramgame.jpg\")
The Tangram craze<\/strong><\/h4>\n
An educational tool harbouring a paradox or two<\/strong><\/h4>\n
![\"\"](\"https:\/\/world.edu\/wp-content\/uploads\/2022\/12\/2MONKSPARADOX.jpg\")
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