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What Is a Tangram?

A tangram is a puzzle of seven geometric pieces, called tans, cut from a single square. Rearranged, the same seven pieces form thousands of silhouettes: animals, people, houses, boats, letters and abstract shapes. The puzzle looks trivial — seven pieces, no picture, no interlocking tabs — and that is exactly its charm: all of the difficulty is in seeing the shape differently.

The 7 tangram pieces

Rectangle

Tangram Rectangle puzzle silhouette
Show solutionTangram Rectangle solution

Triangle

Tangram Triangle puzzle silhouette
Show solutionTangram Triangle solution

Diamond

Tangram Diamond puzzle silhouette
Show solutionTangram Diamond solution

The 7 tangram pieces

The pieces are related by area in a neat way. If a small triangle has area 1, then the square, the parallelogram and the medium triangle each have area 2, each large triangle has area 4, and the whole set has area 16. This is why the two large triangles always cover half of any figure, and why the two small triangles can substitute for the square, the medium triangle or the parallelogram.

The rules

Use all seven pieces in every figure. Pieces must lie flat, they may touch but must never overlap, and the finished shape must match the silhouette. Pieces can be rotated freely and flipped over — flipping is essential, because the parallelogram's mirror image cannot be made by rotation alone.

Why teachers and parents use it

A tangram set is a geometry lesson disguised as a toy. Children meet right angles, halves and quarters, congruence and symmetry by handling them, not by being told. Solving a silhouette trains spatial reasoning — imagining a shape turned, flipped or split — which is the same skill used in mathematics, drawing, building and reading maps. It also rewards patience: most figures fail two or three times before they work.

A short history

The tangram comes from China, where it is called qīqiǎobǎn — roughly, “seven boards of skill”. It became a widespread craze in the early 19th century: Chinese books of tangram figures were printed in large numbers, and around 1815–1818 the puzzle travelled on trading ships to Europe and America, where it was briefly as fashionable as any modern viral game. A famous story claims Napoleon played tangram in exile on Saint Helena; there is no solid evidence for it, but the story itself shows how famous the puzzle had become. The origin of the English word “tangram” is uncertain — one guess links it to the Tang dynasty, another to an old word for a prostitute combined with the Greek -gram; nobody really knows, and any source that sounds sure is guessing.

Tangram and the Stomachion

The tangram is not the only ancient dissection puzzle. The Stomachion, attributed to Archimedes, cuts a square into 14 pieces — triangles and quadrilaterals of many sizes — and was studied for the number of ways the pieces reassemble into the square (17,152 ways, counted only in 2003 with computer help). The tangram is younger and stricter: 7 pieces, all built from right isosceles triangles, which is why its figures stay chunky and readable. If the tangram starts to feel easy, the Stomachion is the traditional next step.

FAQ

Why is it called a tangram?
The origin of the English name is uncertain; the Chinese name, qīqiǎobǎn, means “seven boards of skill”.
Is the tangram good for kids?
Yes. It builds spatial reasoning, shape recognition, fractions intuition and patience, from preschool to primary school.
How many shapes can you make with a tangram?
Thousands of published silhouettes exist, and only a small fraction have been catalogued. This site publishes 19, each verified by computer.
What is the hardest part of tangram?
Seeing past the obvious. Most stuck moments come from one early piece placed in a believable but wrong position — and from forgetting to flip the parallelogram.

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