Tangrams can demonstrate the Pythagorean theorem. The yellow figure in the diagram above is a right triangle; the seven pieces that make up the square on the hypotenuse can be rearranged to form squares on the other two sides.

The third-century mathematician Liu Hui used to explain the theorem by dissecting and rearranging squares. Proper tangrams did not appear until centuries later, but modern Chinese mathematician Liu Dun writes, “We can hypothesize that the inventor of the Tangram, if not a mathematician, was at least inspired or enlightened by” this practice.

(From Jerry Slocum, The Tangram Book, 2003.)