Tangram

The tangram is a dissection puzzle made of seven flat pieces called tans, which are combined to create various shapes. The goal is to match a pattern shown only as an outline, using all seven pieces without overlapping, or to invent original minimalist designs that can be appreciated for their beauty or used to challenge others to replicate their outlines. It is one of the world’s most famous dissection puzzles, serving purposes in entertainment, art, and education. The puzzle is thought to have been invented in China around the late 1700s, and soon after, trading ships brought it to America and Europe. It enjoyed a period of great popularity in Europe, and later saw a resurgence during World War I.

The origin of the English word “tangram” is uncertain. One theory suggests it combines the Greek element “-gram,” meaning something drawn or written, with “tan-” possibly from Chinese *t’an* (to extend) or Cantonese *t’ang* (Chinese). Another idea is that it comes from an archaic English word “tangram,” meaning an odd, intricately contrived thing. The first known use of the word appears in the 1848 book *Geometrical Puzzle for the Young* by mathematician and future Harvard president Thomas Hill, who likely coined it. Hill promoted the term in articles advocating for the puzzle’s educational use, and in 1864 it was officially recognized in Noah Webster’s *American Dictionary*.

Despite its recent arrival in the West, China had a much older tradition of dissection amusements that likely inspired it. The modular banquet tables of the Song dynasty closely resemble tangram pieces, and books existed on arranging them into pleasing patterns. Chinese sources often mention Song dynasty polymath Huang Bosi, who created entertainment for his guests using six small tables called “feast tables” or “swallow tables.” One diagram shows these as oblong rectangles, and some reports say a seventh table was added later, possibly by another inventor. Western sources, however, state that the historical Chinese inventor is unknown except through the pen name Yang-cho-chu-shih (meaning “Dim-witted recluse”). The puzzle is believed to have first appeared in a book titled *Ch’i chi’iao t’u*, which was already reported lost by 1815. It is generally thought the puzzle was invented about twenty years earlier. The third-century mathematician Liu Hui used construction proofs in his work, some of which resemble the later banquet tables that seem to anticipate the tangram. While there is no evidence tangrams were used to prove the Pythagorean theorem, this geometric reasoning likely influenced Chinese culture and led to the puzzle. Early attempts to date the tangram were confused by Samuel Loyd’s 1908 book *The Eighth Book of Tan*, a popular but fraudulent history. Its whimsical claims aroused both interest and suspicion, and by 1910 it was exposed as a hoax. A letter from Oxford Dictionary editor Sir James Murray to puzzlist Henry Dudeney stated that Chinese scholars found no trace of the man Tan, the god Tan, or the Book of Tan in Chinese literature or tradition. Loyd’s claim that the puzzle was 4,000 years old was entirely baseless.

The earliest known tangram was given to Philadelphia shipping magnate Francis Waln in 1802, but the puzzle did not reach a wide Western audience until over a decade later. In 1815, American Captain M. Donnaldson received a pair of books on the subject (one of problems, one of solutions) from author Sang-Hsia-koi while his ship, the *Trader*, was docked there. These were brought to Philadelphia in February 1816, and the first American tangram book was based on them. The puzzle then reached England and became very fashionable, quickly spreading to other European countries, largely due to two British books: *The Fashionable Chinese Puzzle* and its solution book, *Key*. Soon, tangram sets were exported from China in great numbers, made from materials like glass, wood, and tortoise shell. Many of these unusual sets reached Denmark, where interest surged around 1818 with the publication of two books. The first, *Mandarinen* (About the Chinese Game), was a non-fiction work by a Copenhagen University student on the puzzle’s history and popularity. The second, *Det nye chinesiske Gaadespil* (The New Chinese Puzzle Game), contained 339 puzzles copied from *The Eighth Book of Tan* plus one original.