Tangrams: 330 Puzzles

Dover Publications mostly publishes reprints, but this is an original work, first published in 1965 and still going strong. Its author is a Canadian mathematician, now aged 91, who I hope doing as well as his book.

A set of tangrams consists of seven pieces dissected from a square — five isosceles right triangles (two big, one medium, and one small), a square, and a parallelogram. They can be rearranged to form an amazing variety of shapes. The author gives representations of the letters of the alphabet, the digits, birds, fish, animals, boats, household furniture, a pool player, and on and on. They are given all in black with no indication of how they were arrived at, and the puzzle is to reproduce them. The book does not come with a physical set of tangrams but there are pages and pages of them for sale at Amazon. Or, you can download one of several tangram apps.

Tangrams came from China. In The Eighth Book of Tan (1903) the puzzle creator and marketer Sam Loyd (1841–1911) gave a fanciful history, alleging them to be several millennia old, but he was, I think, just having a little fun. (You had to watch Loyd. He would have liked you to believe that he was the inventor of the 15 Puzzle and of Parcheesi, neither of which was so.) An American ship captain brought an 1813 Chinese tangram book back with him from Canton in 1815, and books on tangrams were published in Italy, France, and the United States in 1817. From time to time, though not recently, tangrams have been all the rage, and they have entered into the standard puzzle repertory.

Unlike, say, Rubik’s cube, they haven’t inspired much mathematics. A 1942 paper in the Monthly showed that they could be arranged to form only thirteen convex polygons, but that seems to be all.

The book has some nice text, but its first ninety-two pages are mainly pictures of shapes to be made with the tans, as some people refer to the seven pieces. There follow sixty pages of solutions. A more thorough treatment, The Tangram Book by Jerry Slocum and others (Sterling, 2003), is now out of print.

It seems that today’s audience for tangrams is mainly children. If you want to give your child something to do that could be entertaining and mind-developing, lock up all of his or her screens, and present this book and a set of tangrams. Screams, of delight or outrage, are sure to follow.

Woody Dudley’s parents neglected his development by never providing him with a set of tangrams. Oh, what might have been!