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The New Version of the Tangram Puzzle

The New Version of the Tangram Puzzle. Lecturer ： Wen-Hsien SUN President of Chiu Chang Mathematics Education Foundation. Classic Chinese Tangram.

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The New Version of the Tangram Puzzle

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  1. The New Version of the Tangram Puzzle Lecturer：Wen-Hsien SUN Presidentof Chiu Chang Mathematics Education Foundation

  2. Classic Chinese Tangram • Tangram is a kind of jigsaw puzzle: assemble seven geometric pieces, without overlap, to form charming, elegant, sophisticated, and sometimes paradoxical figures. • We can obtain a set of the Tangram by dissecting a square into seven pieces as the figure shown below.

  3. Classic Chinese Tangram The seven pieces can be rearranged to form thousands of different figures of geometric shapes (triangles, parallelograms, polygons and etc.), people in motion, animals(cats, dogs,pigs, horses and etc.), and bridges, houses, pagodas, letters of the alphabet and some Chinese characters.

  4. Challenges～

  5. Arrange the following shapes using Tangram:

  6. Tangram Facts

  7. Early Tangram The 14 pieces puzzle on the right can be seen as an early version of Tangram. It was first referred in Archimedes’ work in 3rd century BC as “Stomachion,” meaning ‘problem that makes one insane’.A discovery in 1906 in Saint Sabba of Jerusalem shows the puzzle was dissected from a big square not the previously known two smaller squares.

  8. 蝶几圖 • The book, “蝶几圖” written in 1617by Chinese author 戈汕, included the following puzzle. The set contains 13 pieces, with extra piece for the two * marked pieces below.

  9. Pythagorean Theorem Prove the Pythagorean Theorem using two sets of Tangram:

  10. Tangram Table The Tangram table (rosewood) below was made in 1840, Guangdong, China. There is another similar Tangram table with detail carvings on mahoganywood in Taiwan.

  11. Ivory Tangram There are also ivory made Tangram for the royals.

  12. Ivory Tangram This is an ivory Tangram made in 1802 exporting to France.

  13. Ivory Tangram The ivory Tangram on the right was made in England, with gold leaf plating on the surface.

  14. Japanese Tangram: 智慧板 The Japanese Tangram published in Japan, 1796:

  15. Puzzle from China “The Fashionable Chinese Puzzle,” published in 1817 across Europe and America.

  16. Napoleon and Tangram The Swiss. And Dutch books about Tangram reported that Napoleon also likes Tangram.

  17. Left: Dutch Stamps, 1997, with Chinese zodiac made by Tangram. Right: Finnish stamp set, May 2000. Tangram Stamps

  18. Hong Kongstamp set, May 2009. The stamp sheetlet uses the tangram to demonstrate different actions, such as diving, playing football and practicing martial arts, hence showing the versatility and endless possibilities of the game. Tangram Stamps

  19. Tangram Crafts Ceramic containers in the shape of Tangram.

  20. Tangram in France

  21. Book of Tangram Chinese book: 七巧圖解, published in 1815.

  22. The Basic Construction of Tangram Chinese Tangram is an intelligent puzzle based on isosceles right triangles. There is only one monotan (the unit triangles), but there are 3 ditans (formed of 2 unit triangles), 4 tritans (formed of 3 unit triangles) and 14 tetratans (formed of 4 unit triangles).

  23. Japanese Tangram

  24. Shape by Shape

  25. The Pieces

  26. Shape by Shape

  27. Shape by Shape

  28. X

  29. Strategy of Solving the Problem • Never satisfied with only one solution. Always try all the possibilities and find all the solutions. • The difference from mathematics to games is that games need one solution only while mathematics requires finding all possible solutions and proving there are no other possible answers.

  30. Puzzles of the Square • Use pieces (a), (b), (c), (d) and (e) to form a bigger square. • Use pieces (b), (c), (d) and (e) to form a square. b a d c e

  31. Puzzles of the Square Suppose that each symmetric triangle has area of 1: square piece (a) and triangle (b) has area of 2; triangle (c) has area of 4; piece (d) and (e) has area of 5. b a c e d

  32. b a e c d b a e c d Puzzles of the Square If there are 2 copies of each of the 5 pieces (a, b, c, d, e), how to assemble all the pieces to form a square?

  33. b a e c d The Method of Analyzing the Area • a+b+c+d+e=2+2+4+5+5=18 units. If the first question is solvable, the length of the sides of such a square is supposed to be

  34. b e c d The Method of Analyzing the Area • b+c+d+e=16 units. If the second question is solvable, the length of the sides of the square should be 2.

  35. b a e c d b a e c d The Method of Analyzing the Area • 2a+2b+2c+2d+2e=36 units. If the last question is solvable, the length of the sides of the square is supposed to be 3.

  36. Solutions The square of 18 units. The square of 16 units.

  37. Solutions The following figure shows one of the solutions to the square of 36 unit isosceles right triangles.

  38. Arnold transformation

  39. Tangram

  40. Tangram

  41. Tangram

  42. Public image Secret image Generated secret image Compress ration=3.2 , PSNR=31.72

  43. Public image Secret image Generated secret image Compress ration=3.2 , PSNR=30.93

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