The ancient Chinese artform of tangram puzzles is a widely-embraced for its ability to improve mathematics, creativity, and problem-solving skills. More than a hundred years ago, they were as famous as Rubik’s Cube. Some have called them “seven pieces of cleverness.” It is said that the Pythagorean theorem was discovered in the Orient with help of tangram puzzles.

It has been played passionately for entertainment or as an educational tool. It is designed to pull the very best from pupils, boosting shape recognition and pattern design skills. Tangram puzzles have a very simple structure. They are easy to operate and clear to understand. It can be utilized to make more than 1,600 different patterns. This is the allure with tangram puzzles.

Tangram puzzles consist of seven geometric pieces called tans which are generally packaged together in the shape of a square. Tangram puzzles can be visualized reverse jigsaw puzzles. That’s because the student begins with a complete set already assembled. The goal is to then separate the pieces and rearrange them in such a way as to create a wide variety of images.

### The 7 Tans in Tangram Puzzles, Technically Speaking

• 5 right triangles: 2 small (hypotenuse of n/2 and sides of n/2√2); 1 medium (hypotenuse of n/√2 and sides of n/2); 2 large (hypotenuse of n and sides of n/√2). The large triangle is 4 times the size of the small triangle, but curiously its perimeter is only 2 times as big!

• 1 square (side of n/2√2).

• 1 parallelogram/rhomboid (sides of n/2 and n/2√2).

Only the parallelogram (or rhomboid) may need to be flipped when forming certain shapes. It has no “reflection symmetry” but only “rotational symmetry,” which is to say that its mirror image can only be obtained by flipping it over.

### Classic Rules for Tangram Puzzles

• All 7 pieces must be used,

• All pieces must lie flat,

• All pieces must be touching,

• No pieces may overlap,

• Pieces may be rotated and/or flipped to form the desired shape.

### The Objective with Tangram Puzzles

Your mission — if you choose to accept — is to put the seven geometric shapes together to form an instructed silhouette. Many tangram puzzles come with a set of illustrated solutions. Of course, there are many other solutions that can be imagined. Alternatives to provided solutions are accepted as long as they have exactly the same outline. The beauty with tangram puzzles is that different tans can be organized to form the same or a very close relative object.

### The Origin of Tangram Puzzles

There is some dispute over when tangram puzzles were invented. Most agree that they were invented by ancient Chinese working people, tracing back to at least the first century BC. They matured with the Ming Dynasty. The well-known American puzzle expert Sam Loyd has said, “According to the Encyclopedia, tangram puzzles have a very long history. It is a pasttime in China, and its history can be traced back to 4000 years ago…” Others point to a more recent history. In 1742, tangram puzzles first appeared in a Japanese publication. A later work was published in China (1813). In an illustration from an Italian book in 1817, a Chinese puzzle player is seen cutting his own tans from cardboard while two others try to solve a geometric problem. American writer Edgar Allan Poe used ivory to make his tangram puzzles. Napoleon played with tangram puzzles during his exile.

### Greater Historical Context with Chinese Games

Ancient China has a very rich gaming culture. Classic Chinese puzzles, such as the Nine Connected Rings, tangram puzzles, Chinese Sliding Block, Six-piece Burr Puzzle, Four People Toy, and others combine mathematics and games perfectly. They are highly suited for intellectual development. Collectively, they exercise geometry, topology, operations research, and other subjects in math. *The History of Chinese Science* by Dr. Joseph Needham mentioned tangram puzzles as “one of the oldest Oriental entertainment.”

### Making Tangram Puzzles

You will need the following supplies: 1. paper (cardstock or other thick paper works best), 2. scissors, 3. ruler, 4. pencil or a printer.

Follow the below steps and above sequential diagram:

• Start by cutting a square piece of paper. Fold one corner of a piece of paper over to the adjacent side. You could also skip the next three steps by finding template for tangram puzzles.

• To finish making the square, cut off the small rectangle.

• Fold the square piece of paper in half, then in half again. This produces a square into quarters. Repeat this step to create a square divided into sixteenths. Unfold the paper.

• Draw the following lines above and cut along them.

• There are now seven tans: a small square, two small isosceles triangles, a medium-sized isosceles triangle, two large isosceles triangles, and a parallelogram. Definitions: an isosceles triangle has two equal angles and two equal sides, a parallelogram is a four-sided shape with each side parallel to its opposite side.

• Arrange the seven tans into a dynamic range of shapes — animals, people, objects, and more. Imagine as many new solutions as you can!