The Tangram has seven pieces. If you take the square piece to have an area equal to one, then the area of all the pieces is eight. The Tangram is not unique, but one of many variations - many being ancient. One of note is Archimedes' Stomachion. The Tangram Book by Jerry Slocum makes a persuasive case that its origin is Chinese dating to around 1800; the book also provides an excellent history of the Tangram. For those interested, another good book is The Tangram by Joost Elffers which has a curious mathematical section, and like Mr. Slocum's work provides a useful bibliography. Several intriguing questions remain. The foremost is who or what inspired Archimedes' version.
For those familiar with Ancient Egypt and have some basic knowledge of Arithmetic and Geometry, the following twelve Tangram constructions yield additional questions. The enlightened reader may also find them to be something of a memory aid*.
The twelve constructions that follow are grouped in three groups of four with each Tangram piece (i.e. the triangle, square, and rhomboid) starting each group. They can be thought of as "3 by 5 cards" used as study aids by an Ancient Egyptian student preparing for exams to become a scribe or priest. Or from a different point of view, before the Square and Compass perhaps there was the Tangram.
The groupings have been arranged by thematic content with objects familiar during the life of Plato — circa 375 B.C. Also included are views of the Pyramids of Giza as seen from several vantage points — the connection to the Tangram is interesting. A proof of the Pythagorean formula for an isosceles triangle using two Tangrams appears afterwards. As something of a historical tangent, the playing boards of two ancient board games, Alquerque ( the forerunner to the modern board game Checkers ) and Nine Men's Morris, have been included for comparison. A board of Nine Men's Morris has been found at Troy, and both the boards of Alquerque and Nine Men's Morris have been found in an Ancient Egyptian temple (18th Dynasty — Kurna Temple). Solutions to the twelve follow. The booklet concludes with a brief look at the Sand Reckoner.
Many today may see this as something of a joke saying that "the Tangram is just a mere toy for the entertainment of children." Perhaps.