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Tangram

Introduction

The tangram is an intellectual puzzle game, originated in China.  It consists of seven pieces, in the shapes of triangles and quadrilaterals.  Tangrams were called 七巧板 or "Chi-Chiao Pan", meaning "the seven intriguing pieces".  The objective of the puzzle game is to form a designated pattern using all the seven pieces together.  There are many patterns which may be formed from the tangram pieces.  These include basic geometric patterns, shapes of animals, and various common objects.

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.  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.  Each of these piece is called a tan.  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.

Using Tangrams for Teaching Geometry and Fractions.

Tangrams can be used as a good teaching tool for teaching Geometry and Fractions.  Students can form various Geometric shapes using tangram pieces.  They would also learn the ratios and relationship of each pieces to another during the process.

Teaching Geometry Using Tangrams

Tangram Stories:

Read these stories as the children solves the tangram patterns.

The Story of a Crow and a Bottle

The First Christmas

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.

Solve these Tangram puzzles:

 Cart Gate Bottle Bowing Boy Rectangle Shoe Sheep Crab Head Apple Tree Urn Ox Running Star Dog Hill Vase Spade Kettle Letter H Walking Person Goat Rodent Kneeling Partridge Butterfly Welcome Snail Shovel Boating Man Musical Note Boots Turkey Sitting Person Shirt Medal Man's Face Windmill Candlestick Christmas Tree Bed Strawberry Square Wine Glass Arrow Pigeon Offering Space Capsule Rabbit Dancer Bowing Elephant Rooster Mountain Range Letter C Lamp Barge Chair Sailboat Gateway Shoe Balance Ferry Double Arrow Top Lady Horse Wrench Stork Key Head Angel Letter K Trapezoid Jar Praying Pear Man's Head Sparrow Triangle Quail Seal Zebra Arch Tent Stairs Iron Ostrich Pentagon Eagle Altar Dam Dagger Dog Wolf Crown Pavillion Flag Headgear Boomarang Runner Radish Helmet Pyramids Pillar Woman's Head Buffalo Indian Carriage Dipper Cactus Dove Barn Gun Hen Drummer Trapezium Flask Torch Lady Dancing Division Ax Bird Ring

 Letters and Numbers:   A  B  C  D  E  F  G  H  I  J  K  L  M  O  P  S  T  W  X  Y  Z  1  3  4  5  6  7  8  9  ^  !  ?  : Tangram Stories: The Story of a Crow and a Bottle The Boy Who Cried Wolf The First Christmas Weighing an Elephant Twelve Days of Christmas

Next:  Making Your Own Tangram Set

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