Sources page biographical material

Leske. Illustriertes Spielbuch für Mädchen. 1864?

Prob. 584-11, pp. 288 & 405: Chinesisches Verwandlungsspiel. Make a square with the tangram pieces. Shows just five of the pieces, but correctly states which two to make two copies of.

Prob. 584-16, pp. 289 & 406. Make an isosceles right triangle with the tangram pieces.

Prob. 584-18/25, pp. 289-291 & 407: Hieroglyphenspiele. Form various figures from various sets of pieces, mostly tangrams, but the given shapes have bits of writing on them so the assembled figure gives a word. Only one of the shapes is as in Boy's Own Book.

Prob. 588, pp. 298 & 410: Etliche Knackmandeln. Another tangram problem like the preceding, not equal to any in Boy's Own Book.

Adams & Co., Boston. Advertisement in The Holiday Journal of Parlor Plays and Pastimes, Fall 1868. Details?? -- photocopy sent by Slocum. P. 6: Chinese Puzzle. The celebrated Puzzle with which a hundred or more symmetrical forms can be made, with book showing the designs. Though not illustrated, this seems likely to be the Tangrams -- ??

Mittenzwey. 1880. Prob. 243-252, pp. 45 & 95-96; 1895?: 272-281, pp. 49 & 97-98; 1917: 272-282, pp. 45 & 92-93. Make a funnel, kitchen knife, hammer, hat with brim being horizontal or hanging down or turned up, church, saw, dovecote, hatchet, square, two equal squares.

J. Murray (editor of the OED). Two letters to H. E. Dudeney (9 Jun 1910 & 1 Oct 1910). The first inquires about the word 'tangram', following on Dudeney's mention of it in his "World's best puzzles" (op. cit. in 2). The second says that 'tan' has no Chinese origin; is apparently mid 19C, probably of American origin; and the word 'tangram' first appears in Webster's Dictionary of 1864. Dudeney, AM, 1917, p. 44, excerpts these letters.

F. T. Wang & C. S. Hsiung. A theorem on the tangram. AMM 49 (1942) 596 599. They determine the 20 convex regions which 16 isosceles right triangles can form and hence the 13 ones which the Tangram pieces can form.

Mitsumasa Anno. Anno's Math Games. (Translation of: Hajimete deau sugaku no ehon; Fufkuinkan Shoten, Tokyo, 1982.) Philomel Books, NY, 1987. Pp. 38-43 & 95-96 show a simplified 5-piece tangram-like puzzle which I have not seen before. The pieces are: a square of side 1; three isosceles right triangles of side 1; a right trapezium with bases 1 and 2, altitude 1 and slant side 2. The trapezium can be viewed as putting together the square with a triangle. 19 problems are set, with solutions at the back.

James Dalgety. Latest news on oldest puzzles. Lecture to Second Meeting on the History of Recreational Mathematics, 1 Jun 1996. 10pp. In 1998, he extracted the two sections on tangrams and added a list of tangram books in his collection as: The origins of Tangram; © 1996/98; 10pp. (He lists about 30 books, eight up to 1850.) In 1993, he was buying tangrams in Hong Kong and asked what they called it. He thought they said 'tangram' but a slower repetition came out 'ta hau ban' and they wrote down the characters and said it translates as 'seven lucky tiles'. He has since found the characters in 19C Chinese tangram books. It is quite possible that Sam Loyd (qv under Murray, above) was told this name and wrote down 'tangram', perhaps adjusted a bit after thinking up Tan as the inventor.

At the International Congress on Mathematical Education, Seville, 1996, the Mathematical Association gave out The 3, 4, 5 Tangram, a cut card tangram, but in a 6 x 8 rectangular shape, so that the medium sized triangle was a 3-4-5 triangle. I modified this in Nov 1999, by stretching along a diagonal to form a rhombus with angles double the angles of a 3-4-5 triangle, so that four of the triangles are similar to 3-4-5 triangles. Making the small triangles be actually 3-4-5, all edges are integral. I made up 35 problems with these pieces. I later saw that Hans Wiezorke has mentioned this dissection in CFF, but with no problems. I distributed this as my present at G4G4, 2000.