Craft, Create, Calculate: Bring Geometry to Life with the Tangram

This post is by Lora Taylor, a 2025-2026 Albert Einstein Distinguished Educator Fellow at the Library of Congress.

Have you ever played with geometric blocks, arranging them into different shapes and figures? Or twisted a Rubik’s Cube around until you solved it? If so, you’ve taken part in a tradition that can be traced as far back as 250 B.C., to Archimedes and his Stomachion puzzle. Geometric puzzles have long been a favorite pastime across centuries and continents. They are not only fun, but they also help us understand how objects can be moved and arranged in relation to the physical space around them. Geometric puzzles also help strengthen problem solving skills, critical thinking, and creativity.

One of the most enduring of these puzzles is the tangram, which consists of seven geometric shapes, or tans, that can be used to create thousands of figures. The origins of this puzzle are not entirely clear, but it may have been created as early as the third century in China. Below you can see a series of photos from a picture book of tangram puzzles published in 1816 titled Qi qiao chu bian he bi.

These tangram puzzles have been a favorite source of entertainment of people all around the world, including some famous historical figures like Napoleon Bonaparte and Charles Lutwidge Dodgson, more well-known by his pen name, Lewis Carroll. In addition to his work as an author, Carroll was also a mathematician, and he was very fond of playing with the tangram puzzle. He is even said to have created the main characters in Alice in Wonderland based on figures created using the tans. The Mad Hatter, the Red Queen, the White Rabbit, the Cheshire Cat, and other characters in the book are all figures that can be represented with the tangram.

The tangram became wildly popular in America in the early 1900s and can be found in books and newspapers from the time. In the examples above, you can see some of the same tangram puzzles published in two different newspapers with instructions on how to make a tangram at home.

During this same period of time, tangrams also appeared in educational resources, such as the World War I-era manual shown above, which encouraged school children to support the war efforts by creating care packages for soldiers that included hand-made items, one of which was a tangram. The manual offers step-by-step instructions for crafting a tangram at home or at school using only cardboard, a ruler, and a cardboard cutter. There is another geometric puzzle included on page 23 in this manual called the “T Puzzle” which is another example of how simple materials and geometry can spark creativity. Follow the instructions and photos below to create your own tangram.

Crafting a Tangram

The instructions for crafting a tangram are as follows:

Step 1: Draw a square on a piece of cardboard or heavy card stock paper. Label the four corners of the square A, B, C, D. The square can be any size, but a post-it note makes a good reference and can also be traced to create a square.

Step 2: Using a ruler, draw a straight-line connecting point A to point C. This will bisect the square creating two triangles.

Step 3: Using a ruler, find and mark at the midpoints on lines A B and B C, the top and right sides of the square. Now connect those two points with a straight line. Label this new line E F.

Step 4: Line up a ruler from point B to point D and begin drawing a line starting at point D but stop when your pencil reaches line E F. Label the point where this new line meets line E F as point G. Label the center of the square where lines A C and D G meet as point X.

Step 5: Measure the length of line X G. Starting from point X, measure and mark this length on line X C. Label this point J. Starting again from point X, measure and mark this length on line X A. Label this point H. This length is slightly more than half the length of lines X C and X A, make sure that you measure starting from point X so that line X H is longer than line H A and line X J is longer than line J C.

Step 6: Using a ruler, connect point E to point H. Now connect point G to point J.

If completed correctly, H E G X will be a square. You can now carefully cut out the seven shapes using a box cutter or a pair of scissors cutting directly on the lines.

Now that you have your seven tans, you can challenge yourself to complete some of the puzzles shown in the newspaper articles above. As you solve the puzzles keep in mind that the tangram is governed by three simple rules: all seven tans must be used, they must all touch one another, but they cannot overlap.

Exploring tangrams through these historical sources helps us see how ideas and inventions travel across time and cultures. The tangram remains a timeless puzzle inviting us to play, create, problem-solve, and discover new ways of telling stories through mathematics. What stories can you tell using the tans?