Sources page biographical material

6.S. TANGRAMS, ET AL.
GENERAL HISTORIES.
Hoffmann. 1893. Chap III, pp. 74 90, 96-97, 111-124 & 128 = Hoffmann-Hordern, pp. 62 79 & 86-87 with several photos. Describes Tangrams and Richter puzzles at some length. Lots of photos in Hordern. Photos on pp. 67, 71, 75, 87 show Richter's: Anchor (1890 1900, = Tangram), Tormentor (1898), Pythagoras (1892), Cross Puzzle (1892), Circular Puzzle (1891), Star Puzzle (1899), Caricature (1890-1900, = Tangram) and four non-Richter Tangrams in Tunbridge ware, ivory, mother-of-pearl and tortoise shell. Hordern Collection, pp. 45-57 & 60, (photos on pp. 46, 49, 50, 52, 54, 56, 60) shows different Richter versions of Tormentor (1880-1900), Pythagoras (1880-1900), Circular Puzzle (1880-1900), Star Puzzle (1880 1900) and has a wood non-Richter version instead of the ivory version in the last photo.

Ronald C. Read. Tangrams -- 330 Puzzles. Dover, 1965. The Introduction, pp. 1-6, is a sketch of the history. Will Shortz says this is the first serious attempt to counteract the mythology created by Loyd and passed on by Dudeney. Read cannot get back before the early 1800s and notes that most of the Loyd myth is historically unreasonable. However, Read does not pursue the early 1800s history in depth and I consider van der Waals to be the first really serious attempt at a history of the subject.

Peter van Note. Introduction. IN: Sam Loyd; The Eighth Book of Tan; (Loyd & Co., 1903); Dover, 1968, pp. v-viii. Brief debunking of the Loyd myth.

Jan van der Waals. History & Bibliography. In: Joost Elffers; Tangram; (1973), Penguin, 1976. Pp. 9 27 & 29 31. Says the Chinese term "ch'i ch'ae" dates from the Chu era ( 740/ 330), but the earliest known Chinese book is 1813. The History reproduces many pages from early works. The Bibliography cites 8 versions of 4 Chinese books (with locations!) from 1813 to 1826 and 18 Western books from 1805 to c1850. The 1805, and several other references, now seem to be errors.

S&B. 1986. Pp. 22 33 discusses loculus of Archimedes, Chie no Ita, Tangrams and Richter puzzles.

Alberto Milano. Due giochi di società dell'inizio dell'800. Rassegna di Studi e di Notizie 23 (1999) 131-177. [This is a publication by four museums in the Castello Sforzesco, Milan: Raccolta delle Stampe Achille Bertarelli; Archivio Fotografico; Raccolte d'Arte Applicata; Museo degli Strumenti Musicali. Photocopy from Jerry Slocum.] This surveys early books on tangrams, some related puzzles and the game of bell and hammer, with many reproductions of TPs and problems.

Jerry Slocum. The Tangram Book. (With Jack Botermans, Dieter Gebhardt, Monica Ma, Xiaohe Ma, Harold Raizer, Dic Sonneveld and Carla van Spluntern.) ©2001 (but the first publisher collapsed), Sterling, 2003. This is the long awaited definitive history of the subject! It will take me sometime to digest and summarize this, but a brief inspection shows that much of the material below needs revision!
Recent research by Jerry Slocum, backed up by The Admired Chinese Puzzle, indicates that the introduction of tangrams into Europe was done by a person or persons in Lord Amherst's 1815-1817 embassy to China, which visited Napoleon on St. Helena on its return voyage. If so, then the conjectural dating of several items below needs to be amended. I have amended my discussion accordingly and marked such dates with ??. Although watermarking of paper with the correct date was a legal requirement at the time, paper might have been stored for some time before it was printed on, so watermark dates only give a lower bound for the date of printing. I have seen several further items dated 1817, but it is conceivable that some material may have been sent back to Europe or the US a few years earlier -- cf Lee.
On 2 Nov 2003, I did the following brief summary of Slocum's work in a letter to an editor. I've made a few corrections and added a citation to the following literature.

Tangrams. The history of this has now been definitely established in Jerry Slocum's new book: The Tangram Book; ©2001 (but the first publisher collapsed), Sterling, 2003. This history has been extremely difficult to unravel because Sam Loyd deliberately obfuscated it in 1903, claiming the puzzle went back to 2000 BC, because the only previous attempt at a history had many errors, and because much of the material doesn't survive, or only a few examples survive. The history covers a wide range in both time and location, as evidenced by the presence of seven co-authors from several countries.

Briefly, the puzzle, in the standard form, dates from about 1800, in China. It is attributed to Yang-cho-chü-shih, but this is a pseudonym, meaning 'dim-witted recluse', and no copies of his work are known. The oldest known example of the game is one dated 1802 in a museum near Philadelphia -- see Lee, below. The oldest known book on the puzzle had a preface by Sang-hsia-ko [guest under the mulberry tree] dated June 1813 and a postscript by Pi-wu-chü-shih dated July 1813. This is only known from a Japanese facsimile of it made in 1839. This book was republished, with a book of solutions, in two editions in 1815 -- one with about four problems per page, the other with about eleven. The latter version was the ancestor of many 19C books, both in China and the west. Another 2 volume version appeared later in 1815. Sang-hsia-ko explicitly says "The origin of the Tangram lies within the Pythagorean theorem".

In 1816, several ships brought copies of the eleven problems per page books to the US, England and Europe. The first western publication of the puzzle is in early 1817 when J. Leuchars of 47 Piccadilly registered a copyright and advertised sets for sale. But the craze was really set off by the publication of The Fashionable Chinese Puzzle and its Key by John and Edward Wallis and John Wallis Jr in March 1817. This included a poem with a note that the game was "the favourite amusement of Ex-Emperor Napoleon". This went through many printings, with some (possibly the first) versions having nicely coloured illustrations. By the end of the year, there were many other books, including examples in France, Italy and the USA.

Dic Sonneveld, one of the co-authors of Slocum's book, managed to locate the tangram and books that had belonged to Napoleon in the Château de Malmaison, outside Paris, but there is no evidence that Napoleon spent much time playing with it. St. Helena was a regular stop for ships in the China trade. Napoleon is recorded as having bought a chess set from one ship and several notables are recorded as having presented Napoleon with gifts of Chinese objects. A diplomatic letter of Jan 1817 records sending an example of the game from St. Helena to Prince Metternich, but this example has not been traced.

The first American book was Chinese Philosophical and Mathematical Trangram by James Coxe, appearing in Philadelphia in August 1817. The word 'trangram' meaning 'an odd, intricately contrived thing' according to Johnson's Dictionary, was essentially obsolete by 1817, but was still in some use in the US. The earliest known use of the word 'tangram' is in Thomas Hill's Geometrical Puzzles for the Young, Boston, 1848. One suspects that he was influenced by Coxe's book, but he may have known that 'T'ang' is the Cantonese word for 'Chinese'. Hill later became President of Harvard University and was an active promoter and inventor of games for classroom use. In 1864, the word was in Webster's Dictionary.

However, the above is the story of the seven-piece tangram that we know today. There is a long background to this, dating back to the 3rd century BC, when Archimedes wrote a letter to Eratosthenes describing a fourteen piece puzzle, known as the Stomachion or Loculus of Archimedes. The few surviving texts are not very clear and there are two interpretations -- in one the standard arrangement of the pieces is a square and in the other it is a rectangle twice as wide as high. There are six (at least) references to the puzzle in the classical world, the last being in the 6th century. The puzzle was used to make a monstrous elephant, a brutal boar, a ship, a sword, etc., etc. The puzzle then disappears, and no form of it appears in the Arabic world, which has always surprised me, given the Arabic interest in patterns.

Further, several eastern predecessors of the tangrams are known. The earliest is a Japanese version of 1742 by Ganriken (or Granreiken) which has seven pieces, attributed (as were many things) to Sei Shonagon, a 10th century courtesan famous for her ingenuity. By the end of the 18th century, three other dissection/arrangement puzzles appeared in Japan, with 15, 19 and 19 pieces, including some semi-circles. An 1804 print by Utamaro shows courtesans playing with some version of the puzzle -- only two copies of this print have been located.

But the basic puzzle idea has its roots in Chinese approaches to the Theorem of Pythagoras and similar geometric proofs by dissection and rearrangement which date back to the 3rd century (and perhaps earlier). But the tangram did not develop directly from these ideas. From the 12th century, there was a Chinese tradition of making "Banquet Tables" in the form of several pieces that could be arranged in several ways. The first known Chinese book on furniture, by Huang Po-ssu in 1194, describes a Banquet Table formed of seven rectangular pieces: two long, two medium and three short. In 1617, Ko Shan described 'Butterfly Wing" tables with 13 pieces, including isosceles right triangles, right trapeziums and isosceles trapeziums. In 1856, a Chinese scholar noted the resemblance of these tables with the tangram and a modern Chinese historian of mathematics has observed that half of the butterfly arrangement can be easily transformed into the tangrams. No examples of these tables have survived, but tables (and serving dishes) in the tangram pattern exist and are probably still being made in China.
SPECIFIC ITEMS
Kanchusen. Wakoku Chiekurabe. 1727. Pp. 9 & 28-29: a simple dissection puzzle with 8 pieces. The problem appears to consist of a mitre comprising ¾ of a unit square; 4 isosceles right triangles of hypotenuse 1 and 3 isosceles right triangles of side ½, but the solution shows that all the triangles are the same size, say having hypotenuse 1, and the mitre shape is actually formed from a rectangle of size 1 x 2.

"Ganriken" [pseud., possibly of Fan Chu Sen]. Sei Shōnagon Chie-no-Ita (The Ingenious Pieces by Sei Shōnagon.) (In Japanese). Kyoto Shobo, Aug 1742, 18pp, 42 problems and solutions. Reproduced in a booklet, ed. by Kazuo Hanasaki, Tokyo, 1984, as pp. 19 36. Also reproduced in a booklet, transcribed into modern Japanese, with English pattern names and an English abstract, by Shigeo Takagi, 1989. This uses a set of seven pieces different than the Tangram. S&B, p. 22, shows these pieces. Sei Shōnagon (c965-c1010) was a famous courtier, author of The Pillow Book and renowned for her intelligence. The Introduction is signed Ganriken. S&B say this is probably Fan Chu Sen, but Takagi says the author's real name is unknown.

Utamaro. Interior of an Edo house, from the picture book: The Edo Sparrows (or Chattering Guide), 1786. Reproduced in B&W in: J. Hillier; Utamaro -- Colour Prints and Paintings; Phaidon Press, Oxford, (1961), 2nd ed., 1979, p. 27, fig. 15. I found this while hunting for the next item. This shows two women contemplating some pieces but it is hard to tell if it is a tangram type puzzle, or if perhaps they are cakes. Hiroko and Mike Dean tell me that they are indeed cooking cakes.

Utamaro. Woodcut. 1792. Shows two courtesans working on a tangram puzzle. Van der Waals dated this as 1780, but Slocum has finally located it, though he has only been able to find two copies of it! The courtesans are clearly doing a tangram-like puzzle with 12(?) pieces -- the pieces are a bit piled up and one must note that one of the courtesans is holding a piece. They are looking at a sheet with 10 problem figures on it.

Early 19C books from China -- ??NYS -- cited by Needham, p. 111.

Jean Gordon Lee. Philadelphians and the China Trade 1784-1844. Philadelphia Museum of Art, 1984, pp. 122-124. (Photocopy from Jerry Slocum.) P. 124, item 102, is an ivory tangram in a cardboard box, inscribed on the bottom of the box: F. Waln April 4^th 1802. Robert Waln was a noted trader with China and this may have been a present for his third son Francis (1799 1822). This item is in the Ryerss Museum, a city museum in Philadelphia in the country house called Burholme which was built by one of Robert Waln's sons-in-law.

A New Invented Chinese Puzzle, Consisting of Seven Pieces of Ivory or Wood, Viz. 5 Triangles, 1 Rhomboid, & 1 Square, which may be so placed as to form the Figures represented in the plate. Paine & Simpson, Boro'. Undated, but the paper is watermarked 1806. This consists of two 'volumes' of 8 pages each, comprising 159 problems with no solutions. At the end are bound in a few more pages with additional problems drawn in -- these are direct copies of plates 21, 26, 22, 24, and 28 (with two repeats from plate 22) of The New and Fashionable Chinese Puzzle, 1817. Bound in plain covers. This is in Edward Hordern's collection and he provided a photocopy. Dalgety also has a copy.

Ch'i Ch'iao t'u ho pi (= Qiqiao tu hebi) (Harmoniously combined book of tangram problems OR Seven clever pieces). 1813. (Bibliothek Leiden 6891, with an 1815 edition at British Library 15257 d 13.) van der Waals says it has 323 examples. The 1813 seems to be the earliest Chinese tangram book of problems, with the 1815 being the solutions. Slocum says there was a solution book in 1815 and that the problem book had a preface by Sang hsia K'o (= Sang-xia-ke), which was repeated in the solution book with the same date. Milano mentions this, citing Read and van der Waals/Elffers, and says an example is on the BL. A version of this appears to have been the book given to Napoleon and to have started the tangram craze in Europe. I have now received a photocopy from Peter Rasmussen & Wei Zhang which is copied from van der Waals' copy from BL 15257 d 13. It has a cover, 6 preliminary pages and 28 plates with 318 problems. The pages are larger than the photocopies of 1813/1815 versions in the BL that Slocum gave me, which have 334 problems on 86 pages, but I see these are from 15257 d 5 and 14. I have a version of the smaller page format from c1820s which has 334 problems on 84pp, apparently lacking its first sheet. The problems are not numbered, but given Chinese names. They are identical to those appearing in Wallis's Fashionable Chinese Puzzle, below, except the pages are in different order, two pages are inverted, Wallis replaces Chinese names by western numbers and draws the figures a bit more accurately. Wallis skips one number and adds four new problems to get 323 problems - van der Waals seems to have taken 323 from Wallis.

Shichi kou zu Gappeki [The Collection of Seven Piece Clever Figures]. Hobunkoku Publishing, Tokyo, 1881. This is a Japanese translation of an 1813 Chinese book "recognized as the earliest of existing Tangram book", apparently the previous item. [The book says 1803, but Jerry Slocum reports this is an error for 1813!] Reprinted, with English annotations by Y. Katagiri, from N. Takashima's copy, 1989. 129 problems (but he counts 128 because he omits one after no. 124), all included in my version of the previous item, no solutions.
Anonymous. A Grand Eastern Puzzle. C. Davenporte & Co. Registered on 24 Feb 1817, hence the second oldest English (and European?) tangram book [Slocum, p. 71.] It is identical to Ch'i Ch'iao t'u ho pi, 1815, above, except that plates 25 and 27 have been interchanged. It appears to be made by using Chinese pages and putting a board cover on it. On the front cover is the only English text:
A