Tangram is a geometric dissection puzzle, which has seven flat polygons called tans which can be arranged in various forms. It is one of the most famous puzzles of all time which is a native to China where it is called “the seven boards of skill.” Even though we have no clear traces of its origin when, and how it came into existence, there are some stories related to it.
Legend of tangram
During the 3rd century, a part of China was under the rule of Song dynasty. One of the kings wished to have a glass window in his room for the first time. He ordered his courtier to make one. The courtier searched for one of the finest glassmakers and ordered them to get the work done in a fortnight. After working hard they made a perfect “square” glass which looked elegant, to keep it safe they wrapped it with layers of leather and silk clothes and began their journey towards the royal palace. After travelling through plains and forests they came across a small mountain, during the descent of this mountain one of the glassmakers tumbled over a rock and the glass slipped away. The worried glassmakers approached the glass and found it in pieces, to their luck the glass didn’t shatter instead it broke into fine pieces of a square, parallelogram and five triangles of different sizes. Afraid of being punished, they tried to make a square from the broken pieces. In this process they arranged them into a rectangle, parallelogram and several other shapes, after toiling hard they finally achieved square. One of the glassmakers found that many shapes can be formed from them, so he came up with an idea which can save them. As a part of plan they submitted the broken pieces to the king by seeing which the king grew furious, and when the king was about to punish them they asked for a chance to show what they had found. After their presentation, the king showed enthusiasm to try it for himself. Finding it very interesting, the king rewarded the glassmakers and let them go. Playing with these pieces has become a habitual action for the king.
Later this was made with wood and spread across China. This is one of the stories about the origin of tangram, but the true story is not known.
How and When was Tangram introduced to the world?
American Captain M. Donaldson was the first outsider who had found this puzzle very interesting and wanted to take it home. He was given a pair of Sang-his-k’s tangram books along with the puzzle. After a long journey from Canton harbor, the ship finally docked at Philadelphia in February, 1816.
Donaldson published a Tangram book based on the books he brought which was titled as “The Eight book of tan”. In that, a fictitious story was written according to which Tangram was created 4000 years ago in China by a god named “Tan”. It contained around 600-700 shapes and the difficulty in solving these attracted many people. Thus, it became famous and took over the market in a short time in the United States.
It also reached England where people went crazy about this puzzle and it became a fashionable thing. The main reason for its attraction was due to a pair of British Tangram books named “The Fashionable Chinese Puzzle” that had solutions in it. Soon it reached other European countries and got a huge response. One more fact is that Catholic Church used to refuse recreational activities on Sabbath but they didn’t show any objection to tangram which boosted its popularity to sky-high.
It was introduced to Germany in 1891 by an industrialist, Adolf Ritcher with the name “The Anchor Puzzle” which is made out of earthen materials and stones. The craze of tangram continued to grow in European countries but still it was not known to many. It got an international reputation on the stage of World War-I.
Math in it
Apart from common people and industrialists, it has also drawn the attention of many mathematicians around the world as it is not just a common puzzle but also has mathematics in it. If you observe, Tangram is not just a fun puzzle, it also teaches many mathematical concepts. Introducing it to students helps them solve mathematical problems in an interesting way rather than following boring methods.
What can we learn from tangrams?
Tangram gives basic to mid-level concepts of math such as Mensuration, Fractions, Geometry, Sets.
Tangram is made of seven flat (2-dimensional) pieces which are polygons. The polygons present in tangram are of a simple polygon (where an enclosed figure consists of straight and non-intersecting lines). Tangram has three types of right isosceles triangles of small, medium, and large triangles, a square, and a parallelogram total of seven polygons.
The seven polygons have a unique feature that is the angles, when looking at the angels we have a right isosceles triangle(two sides and two angles are equal) where two sides meet at angle 900 and the remaining angles are made at the other ends is 450. There are five such tans in which two are small, one is of medium and two are large right isosceles triangle tans.
If you consider the area of one small triangle as 1 unit, then two such pieces cover one medium triangle, four such pieces cover a large triangle, and not only triangles the small triangle pieces can also cover a square and a parallelogram. So, every shape is covered by a small triangle, it also clears that all angles of tans are multiples of 45o.
Suppose if you consider the length of a side of a square as 1 unit, the area of a square will be 1 sq. unit. Consider this as a basic unit you can find the length of each side of polygons but to find out the length of the longest side of the triangle, we have to use the famous Pythagoras theorem [(Hypotenuse)2 = (side)2 + (side)2] or [a2 + b2 = c2]. This allows the student to explore both concepts of “mensuration” using the “Pythagoras theorem.” After knowing the length of each side now arrange them in any mathematical shape and try to find the area of each shape.
After knowing about the areas, lengths and perimeters, if you start making shapes with tans you will observe that it forms a polygon. Shapes made out of tans form two types of polygons: concave and convex polygons.
Concave Polygon in which one or more vertices points inside so its angle is greater than 180 degrees, almost all the shapes formed by tangram is concave polygon.
Convex polygon in which all of its vertices point outward direction, where no individual internal angle is greater than 180 degree. Among all the shapes formed by tans only 13 convex shapes can be formed.
Fractions can also be explained through tangrams, after knowing the area of a large square i.e., area of tangram we can take an individual polygon and place it in the shape of a square and we can find out what part of the value is the polygon in tangram.
Sets can be explained as a collection of well-defined objects, here in tangram we have a collection of polygons that makes a set, it also has a subset in it which among the polygons triangles forms one set (polygon with three sides) and another set of polygons having four sides square and parallelogram.
Tangram for students
A simple-looking math puzzle with many benefits. Playing with tangrams benefits most of the students who feel geometry is a hard and boring topic, but this helps the students to understand geometry from the basics. At an early age, we can introduce the terms like angles, polygons, lines, etc. It all starts with the observation of polygons, classifying shapes and their properties which creates curiosity towards geometry. We can construct and introduce almost all mathematical figures to students with these seven polygons alone, which helps to know more properties of geometrical figures.
Introducing tangrams to students as a part of the curriculum will enhance problem-solving skills, get them a brief idea of fractions, mensuration, and mathematical vocabulary, which develops a great enthusiasm towards mathematics. Tans can form endless outlines of shapes while arranging them in patterns they imagine which exercises the student’s brain in improving the visual, logical, and puzzle-solving abilities.