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- Bu səhifədəki naviqasiya:
- 6.Q. KNOTTING A STRIP TO MAKE A REGULAR PENTAGON
- 6.R. GEOMETRIC FALLACIES
- 6.R.1. EVERY TRIANGLE IS ISOSCELES
- 6.R.2. A RIGHT ANGLE IS OBTUSE
- 6.R.3. LINES APPROACHING BUT NOT MEETING
- The Fashionable Chinese Puzzle
- Chinese Philosophical and Mathematical Trangram
6.P.2. OTHER TYPES In several early examples, the authors appear unaware that area has vanished! Pacioli. De Viribus. c1500. Ff. 189v - 191r. Part 2. LXXIX. Do(cumento). un tetragono saper lo longare con restregnerlo elargarlo con scortarlo (a tetragon knows lengthening and contraction, enlarging with shortening ??) = Peirani 250-252. Convert a 4 x 24 rectangle to a 3 x 32 using one cut into two pieces. Pacioli's description is cryptic but seems to have two cuts, making d c three pieces. There is a diagram at the bottom of f. 190v, badly k f e redrawn on Peirani 458. Below this is a inserted note which Peirani 252 simply mentions as difficult to read, but can make sense. The g points are as laid out at the right. abcd is the original 4 x 24 h a o b rectangle. g is one unit up from a and e is one unit down from c. Cut from c to g and from e parallel to the base, meeting cg at f. Then move cdg to fkh and move fec to hag. Careful rereading of Pacioli seems to show he is using a trick! He cuts from e to f to g. then turns over the upper piece and slides it along so that he can continue his cut from g to h, which is where f to c is now. This gives three pieces from a single cut! Pacioli clearly notes that the area is conserved. Although not really in this topic, I have put it here as it seems to be a predecessor of this topic and of 6.AY. Sebastiano Serlio. Libro Primo d'Architettura. 1545. This is the first part of his Architettura, 5 books, 1537-1547, first published together in 1584. I have seen the following editions. With French translation by Jehan Martin, no publisher shown, Paris, 1545, f. 22.r. ??NX 1559. F. 15.v. Francesco Senese & Zuane(?) Krugher, Venice, 1566, f. 16.r. ??NX Jacomo de'Franceschi, Venice, 1619, f. 16.r. Translated into Dutch by Pieter Coecke van Aelst as: Den eerstē vijfsten boeck van architecturē; Amsterdam, 1606. This was translated into English as: The Five Books of Architecture; Simon Stafford, London, 1611 = Dover, 1982. The first Booke, f. 12v. 3 x 10 board is cut on a diagonal and slid to form a 4 x 7 table with 3 x 1 left over, but he doesn't actually put the two leftover pieces together nor notice the area change! Pietro Cataneo. L'Architettura di Pietro Cataneo Senese. Aldus, Venice, 1567. ??NX. Libro Settimo. P. 164, prop. XXVIIII: Come si possa accresciere una stravagante larghezza. Gives a correct version of Serlio's process. P. 165, prop. XXX: Falsa solutione del Serlio. Cites p. xxii of Serlio. Carefully explains the error in Serlio and says his method is "insolubile, & mal pensata". Schwenter. 1636. Part 15, ex. 14, p. 541: Mit einem länglichten schmahlen Brett / für ein bräites Fenster einen Laden zu machen. Cites Gualtherus Rivius, Architectur. Discusses Serlio's dissection as a way of making a 4 x 7 from a 3 x 10 but doesn't notice the area change. Gaspar Schott. Magia Universalis. Joh. Martin Schönwetter, Bamberg, Vol. 3, 1677. Pp. 704-708 describes Serlio's error in detail, citing Serlio. ??NX of plates. I have a vague reference to the 1723 ed. of Ozanam, but I have not seen it in the 1725 ed. -- this may be an error for the 1778 ed. below. Minguet. 1755. Pp. not noted -- ??check (1822: 145-146; 1864: 127-128). Same as Hooper. Not in 1733 ed. Vyse. Tutor's Guide. 1771? Prob. 8, 1793: p. 304, 1799: p. 317 & Key p. 358. Lady has a table 27 square and a board 12 x 48. She cuts the board into two 12 x 24 rectangles and cuts each rectangle along a diagonal. By placing the diagonals of these pieces on the sides of her table, she makes a table 36 square. Note that 362 = 1296 and 272 + 12 x 48 = 1305. Vyse is clearly unaware that area has been created. By dividing all lengths by 3, one gets a version where one unit of area is lost. Note that 4, 8, 9 is almost a Pythagorean triple. William Hooper. Rational Recreations. 1774. Op. cit. in 4.A.1. Vol. 4, pp. 286 287: Recreation CVI -- The geometric money. 3 x 10 cut into four pieces which make a 2 x 6 and a 4 x 5. (The diagram is shown in Gardner, MM&M, pp. 131 132.) (I recently saw that an edition erroneously has a 3 x 6 instead of a 2 x 6 rectangle. This must be the 1st ed. of 1774, as it is correct in my 2nd ed. of 1782.) Ozanam-Montucla. 1778. Transposition de laquelle semble résulter que le tout peut être égal à la partie. Prob. 21 & fig. 127, plate 16, 1778: 302-303 & 363; 1803: 298-299 & 361; 1814: 256 & 306; 1840: omitted. 3 x 11 to 2 x 7 and 4 x 5. Remarks that M. Ligier probably made some such mistake in showing 172 = 2 x 122 and this is discussed further on the later page. E. C. Guyot. Nouvelles Récréations Physiques et Mathématiques. Nouvelle éd. La Librairie, Rue S. André des Arcs[sic], Paris, Year 7 [1799]. Vol. 2, Deuxième récréation: Or géométrique -- construction, pp. 41 42 & plate 6, opp. p. 37. Same as Hooper. Manuel des Sorciers. 1825. Pp. 202-203, art. 19. ??NX Same as Hooper. The Boy's Own Book. The geometrical money. 1828: 413; 1828-2: 419; 1829 (US): 212; 1855: 566 567; 1868: 669. Same as Hooper. Magician's Own Book. 1857. Deceptive vision, pp. 258-259. Same as Hooper. = Book of 500 Puzzles, 1859, pp. 72-73. Illustrated Boy's Own Treasury. 1860. Optics: Deceptive vision, p. 445. Same as Hooper. Identical to Book of 500 Puzzles. Wemple & Company (New York). The Magic Egg Puzzle. ©1880. S&B, p. 144. Advertising card, the size of a small postcard, but with ads for Rogers Peet on the back. Starts with 9 eggs. Cut into four rectangles and reassemble to make 6, 7, 8, 10, 11, 12 eggs. R. March & Co. (St. James's Walk, Clerkenwell). 'The Magical Egg Puzzle', nd [c1890]. (I have a photocopy.) Four rectangles which produce 6, 7, ..., 12 eggs. Identical to the Wemple version, but with Wemple's name removed. I only have a photocopy of the front of this and I don't know what's on the back. I also have a photocopy of the instructions. Loyd. US Patent 563,778 -- Transformation Picture. Applied: 11 Mar 1896; patented: 14 Jul 1896. 1p + 1p diagrams. Simple rotating version using 8 to 7 objects. Loyd. Get Off the Earth. Puzzle notices in the Brooklyn Daily Eagle (26 Apr 3 May 1896), printing individual Chinamen. Presenting all of these at an office of the newspaper gets you an example of the puzzle. Loyd ran discussions on it in his Sunday columns until 3 Jan 1897 and he also sold many versions as advertising promotions. S&B, p. 144, shows several versions. Loyd. Problem 17: Ye castle donjon. Tit Bits 31 (6 & 27 Feb & 6 & 20 Mar 1897) 343, 401, 419 & 455. = Cyclopedia, 1914, The architect's puzzle, pp. 241 & 372. 5 x 25 to area 124. Dudeney. Great puzzle crazes. Op. cit. in 2. 1904. Discusses and shows Get Off the Earth. Ball. MRE, 4th ed., 1905, pp. 50-51: Turton's seventy-seven puzzle. Additional section describing Captain Turton's 7 x 11 to 7 x 11 with one projecting square, using bevelled cuts. This is dropped from the 7th ed., 1917. William F. White. 1907 & 1908. See entries in 6.P.1. Dudeney. The world's best puzzles. Op. cit. in 2. 1908. Gives "Get Off the Earth" on p. 785. Loyd. Teddy and the Lions. Gardner, MM&M, p. 123, says he has seen only one example, made as a promotional item for the Eden Musee in Manhattan. This has a round disc, but two sets of figures -- 7 natives and 7 lions which become 6 natives and 8 lions. Dudeney. A chessboard fallacy. The Paradox Party. Strand Mag. 38 (No. 228) (Dec 1909) 676 (= AM, prob. 413, pp. 141 & 247). (There is a solution in Strand Mag. 39 (No. 229) (Jan 1910) ??NYS.) 8 x 8 into 3 pieces which make a 9 x 7. Fun's Great Baseball Puzzle. Will Shortz gave this out at IPP10, 1989, as a colour photocopy, 433 x 280 mm (approx. A3). ©1912 by the Press Publishing Co (The New York World). I don't know if Fun was their Sunday colour comic section or what. One has to cut it diagonally and slide one part along to change from 8 to 9 boys. Loyd. The gold brick puzzle. Cyclopedia, 1914, pp. 32 & 342 (= MPSL1, prob. 24, pp. 22 & 129). 24 x 24 to 23 x 25. Loyd. Cyclopedia. 1914. "Get off the earth", p. 323. Says over 10 million were sold. Offers prizes for best answers received in 1909. Loyd Jr. SLAHP. 1928. "Get off the Earth" puzzle, pp. 5 6. Says 'My "Missing Chinaman Puzzle"' of 1896. Gives a simple and clear explanation. John Barnard. The Handy Boy's Book. Ward, Lock & Co., London, nd [c1930?]. Some interesting optical illusions, pp. 310-311. Shows a card with 11 matches and a diagonal cut so that sliding it one place makes 10 matches. W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. No. 24: A chessboard fallacy, pp. 28-29. 8 x 8 cut with a diagonal of a 8 x 7 region, then pieces slid and a triangle cut off and moved to the other end to make a 9 x 7. Clear illustration. Mel Stover. From 1951, he devised a number of variations of both Get off the Earth (perhaps the best is his Vanishing Leprechaun) and of Teddy and the Lions (6 men and 4 glasses of beer become 5 men and 5 glasses). I have examples of some of these from Stover and I have looked at his notebooks, which are now with Mark Setteducati. See Gardner, MM&M, pp. 125-128. Gardner. SA (May 1961) c= NMD, chap. 11. Mentioned in Workout, chap. 27. Describes his adaptation of a principle of Paul Curry to produce The Disappearing Square puzzle, where 16 or 17 pieces seem to make the same square. The central part of the 17 piece version consists of five equal squares in the form of a Greek cross. The central part of the 16 piece version has four of the squares in the shape of a square. This has since been produced in several places. Ripley's Puzzles and Games. 1966. P. 60. Asserts that when you cut a 2½ x 4½ board into six right triangles with legs 1½ and 2½, then they assemble into an equilateral triangle of edge 5. This has an area loss of about 4%. John Fisher. John Fisher's Magic Book. Muller, London, 1968. Financial Wizardry, pp. 18-19. 7 x 8 region with £ signs marking the area. A line cuts off a triangle of width 7 and height 2 at the top. The rest of the area is divided by a vertical into strips of widths 4 and 3, with a small rectangle 3 by 1 cut from the bottom of the width 3 strip. When the strips are exchanged, one unit of area is lost and one £ sign has vanished. Try-Angle, pp. 126-127. This is one of Curry's triangles -- see Gardner, MM&M, p. 147. Alco-Frolic!, pp. 148-149. This is a form of Stover's 6 & 4 to 5 & 5 version. D. E. Knuth. Disappearances. In: The Mathematical Gardner; ed. by David Klarner; Prindle, Weber & Schmidt/Wadsworth, 1981. P. 264. An eight line poem which rearranges to a seven line poem. Dean Clark. A centennial tribute to Sam Loyd. CMJ 23:5 (Nov 1992) 402 404. Gives an easy circular version with 11 & 12 astronauts around the earth and a 15 & 16 face version with three pieces, a bit like the Vanishing Leprechaun.
Dictionary of Representative Crests. Nihon Seishi Monshō Sōran (A Comprehensive Survey of Names and Crests in Japan), Special issue of Rekishi Dokuhon (Readings in History), Shin Jinbutsu Oraisha, Tokyo, 1989, pp. 271-484. Photocopies of relevant pages kindly sent by Takao Hayashi. Crests 3504 and 3506 clearly show a strip knotted to make a pentagon. 3507 has two such knots and 3508 has five. I don't know the dates, but most of these crests are several centuries old. Lucas. RM2, 1883, pp. 202 203. Tom Tit. Vol. 2, 1892. L'Étoile à cinq branches, pp. 153-154. = K, no. 5: The pentagon and the five pointed star, pp. 20 21. He adds that folding over the free end and holding the knot up to the light shows the pentagram. Vol. 3, 1893. Construire d'un coup de poing un hexagone régulier, pp. 159-161. = K, no. 17: To construct a hexagon by finger pressure, pp. 49 51. Pressing an appropriate size Möbius strip flat gives a regular hexagon. Vol. 3, 1893. Les sept pentagones, pp. 165-166. = K, no. 19: The seven pentagons, pp. 54 55. By tying five pentagons in a strip, one gets a larger pentagon with a pentagonal hole in the middle. Somerville Gibney. So simple! The hexagon, the enlarged ring, and the handcuffs. The Boy's Own Paper 20 (No. 1012) (4 Jun 1898) 573-574. As in Tom Tit, vol. 3, pp. 159-161. Lucas. L'Arithmétique Amusante. 1895. Note IV: Section II: Les Jeux de Ruban, Nos. 1 & 2: Le nœud de cravate & Le nœud marin, pp. 220-222. Cites d'Aviso and says he does both the pentagonal and hexagonal knots, but Lucas only shows the pentagonal one. E. Fourrey. Procédés Originaux de Constructions Géométriques. Vuibert, Paris, 1924. Pp. 113 & 135 139. Cites Lucas and cites d'Aviso as Traité de la Sphère and says he gives the pentagonal and hexagonal knots. Fourrey shows and describes both, also giving the pictures on his title page. F. V. Morley. A note on knots. AMM 31 (1924) 237-239. Cites Knott's translation of Tom Tit. Says the process generalizes to (2n+3) gons by using n loops. Gets even-gons by using two strips. Discusses using twisted strips. Robert C. Yates. Geometrical Tools. (As: Tools; Baton Rouge, 1941); revised ed., Educational Publishers, St. Louis, 1949. Pp. 64-65 gives square (a bit trivial), pentagon, hexagon, heptagon and octagon. Even case need two strips. Donovan A. Johnson. Paper Folding for the Mathematics Class. NCTM, 1957, pp. 16-17: Polygons constructed by tying paper knots. Shows how to tie square, pentagon, hexagon, heptagon and octagon. James K. Brunton. Polygonal knots. MG 45 (No. 354) (Dec 1961) 299 302. All regular n gons, n > 4, can be obtained, except n = 6 which needs two strips. Discusses which can be made without central holes. Marius Cleyet-Michaud. Le Nombre d'Or. Presses Universitaires de France, Paris, 1973. On pp. 47-48, he calls this the 'golden knot' (Le "nœud doré") and describes how to make it. 6.R. GEOMETRIC FALLACIES General surveys of such fallacies can be found in the following. See also: 6.P, 10.A.1. These fallacies are actually quite profound as the first two point out some major gaps in Euclid's axioms -- the idea of a point being inside a triangle really requires notions of order of points on a line and even the idea of continuity, i.e. the idea of real numbers. Ball. MRE. 1st ed., 1892, pp. 31 34, two examples, discussed below. 3rd ed., 1896, pp. 39 46 = 4th ed., 1905, pp. 41-48, seven examples. 5th ed., 1911, pp. 44-52 = 11th ed., 1939, pp. 76-84, nine example. Walther Lietzmann. Wo steckt der Fehler? Teubner, Stuttgart, (1950), 3rd ed., 1953. (Strens/Guy has 3rd ed., 1963(?).) (There are 2nd ed, 1952??; 5th ed, 1969; 6th ed, 1972. MG 54 (1970) 182 says the 5th ed appears to be unchanged from the 3rd ed.) Chap. B: V, pp. 87-99 has 18 examples. (An earlier version of the book, by Lietzmann & Trier, appeared in 1913, with 2nd ed. in 1917. The 3rd ed. of 1923 was divided into two books: Wo Steckt der Fehler? and Trugschlüsse. There was a 4th ed. in 1937. The relevant material would be in Trugschlüsse, but I have not seen any of the relevant books, though E. P. Northrop cites Lietzmann, 1923, three times -- ??NYS.) E. P. Northrop. Riddles in Mathematics. 1944. Chap. 6, 1944: 97-116, 232-236 & 249-250; 1945: 91-109, 215-219 & 230-231; 1961: 98-115, 216-219 & 229. Cites Ball, Lietzmann (1923), and some other individual items. V. M. Bradis, V. L. Minkovskii & A. K. Kharcheva. Lapses in Mathematical Reasoning. (As: [Oshibki v Matematicheskikh Rassuzhdeniyakh], 2nd ed, Uchpedgiz, Moscow, 1959.) Translated by J. J. Schorr-Kon, ed. by E. A. Maxwell. Pergamon & Macmillan, NY, 1963. Chap. IV, pp. 123-176. 20 examples plus six discussions of other examples. Edwin Arthur Maxwell. Fallacies in Mathematics. CUP, (1959), 3rd ptg., 1969. Chaps. II-V, pp. 13-36, are on geometric fallacies. Ya. S. Dubnov. Mistakes in Geometric Proofs. (2nd ed., Moscow?, 1955). Translated by Alfred K. Henn & Olga A. Titelbaum. Heath, 1963. Chap 1-2, pp. 5-33. 10 examples. А. Г. Конфорович. [A. G. Konforovich]. (Математичні Софізми і Парадокси [Matematichnī Sofīzmi ī Paradoksi] (In Ukrainian). Радянська Школа [Radyans'ka Shkola], Kiev, 1983.) Translated into German by Galina & Holger Stephan as: Konforowitsch, Andrej Grigorjewitsch; Logischen Katastrophen auf der Spur – Mathematische Sophismen und Paradoxa; Fachbuchverlag, Leipzig, 1990. Chap. 4: Geometrie, pp. 102-189 has 68 examples, ranging from the type considered here up through fractals and pathological curves. S. L. Tabachnikov. Errors in geometrical proofs. Quantum 9:2 (Nov/Dec 1998) 37-39 & 49. Shows: every triangle is isosceles (6.R.1); the sum of the angles of a triangle is 180o without use of the parallel postulate; a rectangle inscribed in a square is a square; certain approaching lines never meet (6.R.3); all circles have the same circumference (cf Aristotle's Wheel Paradox in 10.A.1); the circumference of a wheel is twice its radius; the area of a sphere of radius R is π2R2.
Ball. MRE, 1st ed., 1892, pp. 33 34. On p. 32, Ball refers to Euclid's lost Fallacies and presents this fallacy and the one in 6.R.2: "I do not know whether either of them has been published previously." In the 3rd ed., 1896, pp. 42-43, he adds the heading: To prove that every triangle is isosceles. In the 5th ed., 1911, p. 45, he adds a note that he believes these two were first published in his 1st ed. and notes that Carroll was fascinated by them and they appear in The Lewis Carroll Picture Book (= Carroll-Collingwood) -- see below. Mathesis (1893). ??NYS. [Cited by Fourrey, Curiosities Geometriques, p. 145. Possibly Mathesis (2) 3 (Oct 1893) 224, cited by Ball in MRE, 3rd ed, 1896, pp. 44-45, cf in Section 6.R.4.] Carroll-Collingwood. 1899. Pp. 264-265 (Collins: 190-191). = Carroll-Wakeling II, prob. 27: Every triangle has a pair of equal sides!, pp. 43 & 27. Every triangle is isosceles. Carroll may have stated this as early as 1888. Wakeling's solution just suggests making an accurate drawing. Carroll-Gardner, p. 65, mentions this and says it was not original with Carroll. Ahrens. Mathematische Spiele. Teubner. Alle Dreiecke sind gleichschenklige. 2nd ed., 1911, chap. X, art. VI, pp. 108 & 119 120. 3rd ed., 1916, chap. IX, art. IX, pp. 92-93 & 109-111. 4th ed., 1919 & 5th ed., 1927, chap IX, art. IX, pp. 99 101 & 116 118. W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. Call Mr. Euclid -- No. 15: To prove all triangles are equilateral, pp. 16-17. Clear exposition of the fallacy. See Read in 6.R.4 for a different proof of this fallacy.
Mittenzwey. 1895?. Prob. 331, pp. 58 & 106; 1917: 331, pp. 53 & 101. Carroll-Collingwood. 1899. Pp. 266 267 (Collins 191-192). An obtuse angle is sometimes equal to a right angle. Carroll-Gardner, p. 65, mentions this and says it was not original with Carroll. H. E. Licks. 1917. Op. cit. in 5.A. Art. 82, p. 56. W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. Call Mr. Euclid -- No. 16: To prove one right angle greater than another right angle, pp. 18-19. "Here again, if you take the trouble to draw an accurate diagram, you will find that the "construction" used for the alleged proof is impossible." E. A. Maxwell. Note 2121: That every angle is a right angle. MG 34 (No. 307) (Feb 1950) 56 57. Detailed demonstration of the error. 6.R.3. LINES APPROACHING BUT NOT MEETING Proclus. 5C. A Commentary on the First Book of Euclid's Elements. Translated by Glenn R. Morrow. Princeton Univ. Press, 1970. Pp. 289-291. Gives the argument and tries to refute it. van Etten/Henrion/Mydorge. 1630. Part 2, prob. 7: Mener une ligne laquelle aura inclination à une autre ligne, & ne concurrera jamais contre l'Axiome des paralelles, pp. 13 14. Schwenter. 1636. To be added. Ozanam-Montucla. 1778. Paradoxe géométrique des lignes .... Prob. 70 & fig. 116-117, plate 13, 1778: 405-407; 1803: 411-413; 1814: 348-350. Prob. 69, 1840: 180-181. Notes that these arguments really produce a hyperbola and a conchoid. Hutton adds that a great many other examples might be found. E. P. Northrop. Riddles in Mathematics. 1944. 1944: 209-211 & 239; 1945: 195 197 & 222; 1961: 197 198 & 222. Gives the 'proof' and its fallacy, with a footnote on p. 253 (1945: 234; 1961: 233) saying the argument "has been attributed to Proclus." Jeremy Gray. Ideas of Space. OUP, 1979. Pp. 37-39 discusses Proclus' arguments in the context of attempts to prove the parallel postulate. 6.R.4. OTHERS Ball. MRE, 3rd ed, 1896, pp. 44-45. To prove that, if two opposite sides of a quadrilateral are equal, the other two sides must be parallel. Cites Mathesis (2) 3 (Oct 1893) 224 -- ??NYS Cecil B. Read. Mathematical fallacies & More mathematical fallacies. SSM 33 (1933) 575 589 & 977-983. There are two perpendiculars from a point to a line. Part of a line is equal to the whole line. Every triangle is isosceles (uses trigonometry). Angle trisection (uses a marked straightedge). P. Halsey. Class Room Note 40: The ambiguous case. MG 43 (No. 345) (Oct 1959) 204 205. Quadrilateral ABCD with angle A = angle C and AB = CD. Is this a parallelogram?
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!
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.
"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 4th 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.
---------- THE following Chineze Puzzle is recommended to the Nobility, Gentry, and others, being superior to any hitherto invented for the Amusement of the Juvenile World, to whom it will afford unceasing recreation and information; being formed on Geometrical principles, it may not be considered as trifling to those of mature years, exciting interest, because difficult and instructive, imperceptibly leading the mind on to invention and per- severence. -- The Puzzle consists of five triangles, a square, and a rhomboid, which may be placed in upwards of THREE HUNDRED and THIRTY Characters, greatly re- sembling MEN, BEASTS, BIRDS, BOATS, BOTTLES, GLASS- ES, URNS, &c. The whole being the unwearied exertion of many years study and application of one of the Lite- rati of China, and is now offered to the Public for their patronage and support. ENTERED AT STATIONERS HALL ----
Published and sold by C. DAVENPORTE and Co. No. 20, Grafton Street, East Euston Square.
PLUS
A Key to the New and Fashionable Chinese Puzzle, Published by J. and E. Wallis, 42, Skinner Street, London, Wherein is explained the method of forming every Figure contained in That Pleasing Amusement. Nd [Mar 1817]. Photocopy from the Bodleian Library, Oxford, catalogue number Jessel e.1176. TP seems to made by pasting in the cover slip and has been bound in as a left hand page. ALSO a photocopy from Jerry Slocum. In the latter copy, the apparent TP appears to be a paste down on the cover. The latter copy does not have the Stanzas mentioned below. Slocum's copy has paper watermarked 1815; I didn't check this at the Bodleian. NOTE. This is quite a different book than The New and Fashionable Chinese Puzzle published by Goodrich in New York, 1817. Bound in at the beginning of the Fashionable Chinese Puzzle and the Bodleian copy of the Key is: Stanzas, Addressed to Messrs. Wallis, on the Ingenious Chinese Puzzle, Sold by them at the Juvenile Repository, 42, Skinner Street. In the Key, this is on different paper than the rest of the booklet. The Stanzas has a footnote referring to the ex-Emperor Napoleon as being in a debilitated state. (Napoleon died in 1821, which probably led to the Bodleian catalogue's date of c1820 for the entire booklet - but see below. Then follow 28 plates with 323 numbered figures (but number 204 is skipped), solved in the Key. In the Bodleian copy of the Key, these are printed on stiff paper, on one side of each sheet, but arranged as facing pairs, like Chinese booklets. [Philip A. H. Brown; London Publishers and Printers c. 1800-1870; British Library, 1982, p. 212] says the Wallis firm is only known to have published under the imprint J. & E. Wallis during 1813 and Ruth Wallis showed me another source giving 1813?-1814. This led me to believe that the booklets originally appeared in 1813 or 1814, but that later issues or some owner inserted the c1820 sheet of Stanzas, which was later bound in and led the Bodleian to date the whole booklet as c1820. Ruth Wallis showed me a source that states that John Wallis (Jun.) set up independently of his father at 186 Strand in 1806 and later moved to Sidmouth. Finding when he moved to Sidmouth might help date this publication more precisely, but it may be a later reissue. However, Slocum has now found the book advertised in the London Times in Mar 1817 and says this is the earliest Western publication of tangrams, based on the 1813/1815 Chinese work. Wallis also produced a second book of problems of his own invention and some copies seem to be coloured. In AM, p. 43, Dudeney says he acquired the copy of The Fashionable Chinese Puzzle which had belonged to Lewis Carroll. He says it was "Published by J. and E. Wallis, 42 Skinner Street, and J. Wallis, Jun., Marine Library, Sidmouth" and quotes the Napoleon footnote, so this copy had the Stanzas included. This copy is not in the Strens Collection at Calgary which has some of Dudeney's papers. Van der Waals cites two other works titled The Fashionable Chinese Puzzle. An 1818 edition from A. T. Goodridge [sic], NY, is in the American Antiquarian Society Library (see below) and another, with no details given, is in the New York Public Library. Could the latter be the Carroll/Dudeney copy? Toole Stott 823 is a copy with the same title and imprint as the Carroll/Dudeney copy, but he dates it c1840. This version is in two parts. Part I has 1 leaf text + 26 col. plates -- it seems clear that col. means coloured, a feature that is not mentioned in any other description of this book -- perhaps these were hand-coloured by an owner. Unfortunately, he doesn't give the number of puzzles. I wonder if the last two plates are missing from this?? Part II has 1 leaf text + 32 col. plates, giving 252 additional figures. The only copy cited was in the library of J. B. Findlay -- I have recently bought a copy of the Findlay sale catalogue, ??NYR. Toole Stott 1309 is listed with the title: Stanzas, .... J. & F. [sic] Wallis ... and Marine Library, Sidmouth, nd [c1815]. This has 1 leaf text and 28 plates of puzzles, so it appears that the Stanzas have been bound in and the original cover title slip is lost or was not recognised by Toole Stott. The date of c1815 is clearly derived from the Napoleon footnote but 1817 would have been more reasonable, though this may be a later reissue. Again only one copy is cited, in the library of Leslie Robert Cole. Plates 1-28 are identical to plates 1-28 of The Admired Chinese Puzzle, but in different order. The presence of the Chinese text in The Admired Chinese Puzzle made me think the Wallis version was later than it. Comparison of the Bodleian booklet with the first 27 plates of Giuoco Cinese, 1818?, reveals strong similarities. 5 plates are essentially identical, 17 plates are identical except for one, two or three changes and 3 plates are about 50% identical. I find that 264 of the 322 figures in the Wallis booklet occur in Giuoco Cinese, which is about 82%. However, even when the plates are essentially identical, there are often small changes in the drawings or the layout. Some of the plates were copied by hand into the Hordern Collection's copy of A New Invented Chinese Puzzle, c1806??.
This ingenious geometrical Puzzle was introduced into this Kingdom from China. The following sheets are a correct Copy from the Chinese Publication, brought to England by a Gentleman of high Rank in the suit [sic] of Lord Amherst's late Embassy. To which are added caricature Designs as an illustration, every figure being emblematical of some Being or Article known to the Chinese. The plates are identical to the plates in The Fashionable Chinese Puzzle above, but in different order and plate 4 is inverted and this version is clearly upside down. Sy Hall. A New Chinese Puzzle, The Above Consists of Seven Pieces of Ivory or Wood, viz. 5 Triangles, 1 Rhomboid, and 1 Square, which will form the 292 Characters, contained in this Book; Observing the Seven pieces must be used to form each Character. NB. This Edition has been corrected in all its angles, with great care and attention. Engraved by Sy Hall, 14 Bury Street, Bloomsbury. 31 plates with 292 problems. Slocum, the Hordern Collection and BL have copies. I have a photocopy from a version from Slocum which has no date but is watermarked 1815. Slocum's recent book [The Tangram Book, pp. 74-75] shows a version of the book with the publisher's name as James Izzard and a date of 1817. Sy probably is an abbreviation of Sydney (or possibly Stanley?). (The BL copy is watermarked IVY MILL 1815 and is bound with a large folding Plate 2 by Hall, which has 83 tinted examples with solution lines drawn in (by hand??), possibly one of four sheets giving all the problems in the book. However there is no relationship between the Plate and the book -- problems are randomly placed and often drawn in different orientation. I have a photocopy of the plate on two A3 sheets and a copy of a different plate with 72 problems, watermarked J. Green 1816.) A New Chinese Puzzle. Third Edition: Universally allowed to be the most correct that has been published. 1817. Dalgety has a copy. A New Chinese Puzzle Consisting of Seven Pieces of Ivory or Wood, The Whole of which must be used, and will form each of the CHARACTERS. J. Buckland, 23 Brook Street, Holborn, London. Paper watermarked 1816. (Dalgety has a copy, ??NYS.) Miss D. Lowry. A Key to the Only Correct Chinese Puzzle Which has Yet Been Published, with above a Hundred New Figures. No. 1. Drawn and engraved by Miss Lowry. Printed by J. Barfield, London, 1817. The initial D. is given on the next page. Edward Hordern's collection has a copy. W. Williams. New Mathematical Demonstrations of Euclid, rendered clear and familiar to the minds of youth, with no other mathematical instruments than the triangular pieces commonly called the Chinese Puzzle. Invented by Mr. W. Williams, High Beech Collegiate School, Essex. Published by the author, London, 1817. [Seen at BL.] Enigmes Chinoises. Grossin, Paris, 1817. ??NYS -- described and partly reproduced in Milano. Frontispiece facing the TP shows an oriental holding a banner which has the pieces and a few problems on it. This is a small book, with five or six figures per page. The figures seem to be copied from the Fashionable Chinese Puzzle, but some figures are not in that work. Milano says this is cited as the first French usage of the term 'tangram', but this does not appear in Milano's photos and it is generally considered that Loyd introduced the word in the 1850s. Milano's phrasing might be interpreted as saying this is the first French work on tangrams. Chinesische-Raethsel. Produced by Daniel Sprenger with designs by Matthaeus Loder, Vienna, c1818. ??NYS -- mentioned by Milano. Chinesisches Rätsel. Enigmes chinoises. Heinrich Friedrich Muller (or Mueller), Vienna, c1810??. ??NYS (van der Waals). This is probably a German edition of the above and should be dated 1817 or 1818. However, Milano mentions a box in the Historisches Museum der Stadt Wien, labelled Grosse Chinesische Raethsel, produced by Mueller and dated 1815-1820. Passe-temps Mathématique, ou Récréation à l'ile Sainte-Hélène. Ce jeu qui occupé à qu'on prétend, les loisirs du fameux exilé à St.-Hélène. Briquet, Geneva, 1817. 21pp. [Copy advertised by Interlibrum, Vaduz, in 1990.] The New and Fashionable Chinese Puzzle. A. T. Goodrich & Co., New York, 1817. TP, 1p of Stanzas (seems like there should be a second page??), 32pp with 346 problems. Slocum has a copy. [Key] to the Chinese Philosophical Amusements. A. T. Goodrich & Co., New York, 1817. TP, 2pp of stanzas (the second page has the Napoleon footnote and a comment which indicates it is identical to the material in the problem book), Index to the Key to the Chinese Puzzle, 80pp of solutions as black shapes with white spacing. Slocum has a copy. NOTE. This is quite a different book than The Fashionable Chinese Puzzle published in London by Wallis in 1817. Slocum writes: "Although the Goodrich problem book has the same title as the British book by Wallis and Goodrich has the "Stanzas" poem (except for the first 2 paragraphs which he deleted) the problem books have completely different layouts and Goodrich's solution book largely copies Chinese books." Il Nuovo e Dilettevole Giuoco Chinese. Bardi, Florence, 1817. ??NYS -- mentioned by Milano. Buonapartes Geliefkoosste Vermaack op St. Helena, op Chineesch Raadsel. 1er Rotterdam by J. Harcke. Prijs 1 - 4 ??. 2e Druck te(?) Rotterdam. Ter Steendrukkery van F. Scheffers & Co. Nanco Bordewijk has recently acquired this and Slocum has said it is a translation of one of the English items in c1818. I have just a copy of the cover, and it uses many fancy letters which I don't guarantee to have read correctly. Recueil des plus jolis Jeux de Sociéte, dans lequel on trouve les gravures d'un grand nombre d'énigmes chinoises, et l'explication de ce nouveau jeu. Chez Audot, Librairie, Paris, 1818. Pp. 158-162: Le jeu des énigmes chinoises. This is a short introduction, saying that the English merchants in Japan have sent it back to their compatriots and it has come from England to France. This is followed by 11 plates. The first three are numbered. The first shows the pieces formed into a rectangle. The others have 99 problems, with 7 shown solved (all six of those on plate 2 and one (the square) on the 10th plate.) Das grosse chinesische Rätselspiel für die elegante Welt. Magazin für Industrie (Leipzig) (1818). ??NYS (van der Waals). Jerry Slocum informs me that 'Magazin' here denotes a store, not a periodical, and that this is actually a game version with a packet of 50 cards of problems, occurring in several languages, from 1818. I have acquired a set of the cards which lacks one card (no. 17), in a card box with labels in French and Dutch pasted on. One side has: Nouvelles / ENIGMES / Chinoises / en Figures et en Paysages with a dancing Chinaman below. The other side has: Chineesch / Raadselspel, / voor / de Geleerde Waereld / in / 50 Beelaachlige / Figuren. with two birds below. Both labels are printed in red, with the dancing Chinaman having some black lines. The cards are 82 x 55 mm and are beautifully printed with coloured pictures of architectonic, anthropomorphic and zoomorphic designs in appropriate backgrounds. The first card has four shapes, three of which show the solution with dotted lines. All other cards have just one problem shape. The reverses have a simple design. Slocum says the only complete set he has seen is in the British Library. I have scanned the cards and the labels. Gioco cinese chiamato il rompicapo. Milan, 1818. ??NYS (van der Waals). Fratelli Bettali, Milan, nd, of which Dalgety has a copy. Al Gioco Cinese Chiamato Il Rompicapo Appendice di Figure Rappresentanti ... Preceduta da un Discorso sul Rompicapo e sulla Cina intitolato Passatempo Preliminare scritto dall'Autore Firenze All'Insegna dell'Ancora 1818. 64pp + covers. The cover or TP has an almond shape with the seven shapes inside. Pp. 3-43 are text -- the Passatempo Preliminare and an errata page. 12 plates. The first is headed Alfabeto in fancy Gothic. Plates 1-3 give the alphabet (J and W are omitted). Plate 4 has the positive digits. Plates 5-12 have facing pages giving the names of the figures (rather orientalized) and contain 100 problems. Hence a total of 133 problems, no solutions. The Hordern collection has a copy and I have a photocopy from it. This has some similarities to Giuoco Cinese. Described and partly reproduced in Milano. Al Gioco Cinese chiamato il Rompicapo Appendice. Pietro & Giuseppe Vallardi, Milan, 1818. Possibly another printing of the item above. ??NYS -- described in Milano, who reproduces plates 1 & 2, which are identical to the above item, but with a simpler heading. Milano says the plates are identical to those in the above item. Nuove e Dilettevole Giuoco Chinese. Milano presso li Frat. Bettalli Cont. del Cappello N. 4031. Dalgety has a copy. It is described and two pages are reproduced in Milano from an example in the Raccolta Bertarelli. Milano dates it as 1818. Cover illustration is the same as The Fashionable Chinese Puzzle, with the text changed. But it is followed by some more text: Questa ingegnosa invenzione è fondata sopra principi Geometrici, e consiste in 7 pezzi cioè 5. triangoli, un quadrato ed un paralellogrammo i quali possono essere combinati in modo da formare piu di 300 figure curiose. The second photo shows a double page identical to pp. 3-4 of The Fashionable Chinese Puzzle, except that the page number on p. 4 was omitted in printing and has been written in. (Quaritch's catalogue 646 (1947) item 698 lists this as Nuovo e dilettevole Giuoco Chinese, from Milan, [1820?]) Nuove e Dilettevole Giuoco Chinese. Bologna Stamperia in pietra di Bertinazzi e Compag. ??NYS -- described and partly reproduced in Milano from an example in the Raccolta Bertarelli. Identical to the above item except that it is produced lithographically, the text under the cover illustration has been redrawn, the page borders, the page numbers and the figure numbers are a little different. Milano's note 5 says the dating of this is very controversial. Apparently the publisher changed name in 1813, and one author claims the book must be 1810. Milano opts for 1813? but feels this is not consistent with the above item. From Slocum's work and the examples above, it seems clear it must be 1818? Supplemento al nuovo giuoco cinese. Fratelli Bettalli, Milan, 1818. ??NYS -- described in Milano, who says it has six plates and the same letters and digits as Al Gioco Cinese Chiamato Il Rompicapo Appendice. Giuoco Cinese Ossia Raccolta di 364. Figure Geometrica [last letter is blurred] formate con un Quadrato diviso in 7. pezzi, colli quali si ponno formare infinite Figure diversi, come Vuomini[sic], Bestie, Ucelli[sic], Case, Cocchi, Barche, Urne, Vasi, ed altre suppelletili domestiche: Aggiuntovi l'Alfabeto, e li Numeri Arabi, ed altre nuove Figure. Agapito Franzetti alle Convertite, Rome, nd [but 1818 is written in by hand]. Copy at the Warburg Institute, shelf mark FMH 4050. TP & 30 plates. It has alternate openings blank, apparently to allow you to draw in your solutions, as an owner has done in a few cases. The first plate shows the solutions with dotted lines, otherwise there are no solutions. There is no other text than on the TP, except for a florid heading Alfabeto on plate XXVIII. The diagrams have no numbers or names. The upper part of the TP is a plate of three men, intended to be Orientals, in a tent? The one on the left is standing and cutting a card marked with the pieces. The man on the right is sitting at a low table and playing with the pieces. He is seated on a box labelled ROMPI CAPO. A third man is seated behind the table and watching the other seated man. On the ground are a ruler, dividers and right angle. The Warburg does not know who put the date 1818 in the book, but the book has a purchase note showing it was bought in 1913. James Dalgety has the only other copy known. Sotheby's told him that Franzetti was most active about 1790, but Slocum finds Sotheby's is no longer very definite about this. I thought it possible that a page was missing at the beginning which gave a different form of the title, but Dalgety's copy is identical to this one. Mario Velucchi says it is not listed in a catalogue of Italian books published in 1800-1900. The letters and numbers are quite different to those shown in Elffers and the other early works that I have seen, but there are great similarities to The New and Fashionable Chinese Puzzle, 1817 (check which??), and some similarities to Al Gioco Cinese above. I haven't counted the figures to verify the 364. Mentioned in Milano, based on the copy I sent to Dario Uri. Jeu du Casse Tete Russe. 1817? ??NYS -- described and partly reproduced in Milano from an example in the Raccolta Bertarelli but which has only four cards. Here the figures are given anthropomorphic or architectonic shapes. There are four cards on one coloured sheet and each card has a circle of three figures at the top with three more figures along the bottom. Each card has the name of the game at the top of the circle and "les secrets des Chinois dévoliés" and "casse tête russe" inside and outside the bottom of the circle. The figures are quite different than in the following item. Nuovo Giuoco Russo. Milano presso li Frat. Bettalli Cont. del Cappello. [Frat. is an abbreviation of Fratelli (Brothers) and Cont. is an abbreviation of Contrade (road).] Box, without pieces, but with 16 cards of problems (one being examples) and instruction sheet (or leaflet). ??NYS - described by Milano with reproductions of the box cover and four of the cards. This example is in the Raccolta Bertarelli. Box shows a Turkish(?) man handing a box to another. On the first card is given the title and publisher in French: Le Casse-Tête Russe Milan, chez les Fr. Bettalli, Rue du Chapeau. The instruction sheet says that the Giuoco Chinese has had such success in the principal cities of Europe that a Parisian publisher has conceived another game called the Casse Tête Russe and that the Brothers Bettalli have hurried to produce it. Each card has four problems where the figures are greatly elaborated into architectonic forms, very like those in Metamorfosi, below. Undated, but Milano first gives 1815 1820, and feels this is closely related to Metamorfosi and similar items, so he concludes that it is 1818 or 1819, and this seems to be as correct as present knowledge permits. The figures are quite different than in the French version above. Metamorfosi del Giuoco detto l'Enimma Chinese. Firenze 1818 Presso Gius. Landi Libraio sul Canto di Via de Servi. Frontispiece shows an angel drawing a pattern on a board which has the seven pieces at the top. The board leans against a plinth with the solution for making a square shown on it. Under the drawing is A. G. inv. Milano reproduces this plate. One page of introduction, headed Idea della Metamorfosi Imaginata dell'Enimma Chinese. 100 shapes, some solved, then with elegant architectonic drawings in the same shapes, signed Gherardesce inv: et inc: Milano identifies the artist as Alessandro Gherardesca (1779-1852), a Pisan architect. See S&B, pp. 24 25. Grand Jeu du Casse Tête Français en X. Pieces. ??NYS -- described and partly reproduced in Milano, who says it comes from Paris and dates it 1818? The figures are anthropomorphic and are most similar to those in Jeu du Casse Tete Russe. Grande Giuocho del Rompicapo Francese. Milano presso Pietro e Giuseppe Vallardi Contrada di S. Margherita No 401(? my copy is small and faint). ??NYS -- described and partly reproduced in Milano, who dates it as 1818-1820. Identical problems as in the previous item, but the figures have been redrawn rather than copied exactly. Ch'i Ch'iao pan. c1820. (Bibliothek Leiden 6891; Antiquariat Israel, Amsterdam.) ??NYS (van der Waals). Le Veritable Casse tete, ou Enigmes chinoises. Canu Graveur, Paris, c1820. BL. ??NYS (van der Waals). L'unico vero Enimma Chinese Tradotto dall'originale, pubblicato a Londra, da J. Barfield. Florence, [1820?]. [Listed in Quaritch's catalogue 646 (1947) item 699.) A tangram appears in Pirnaisches Wochenblatt of 16 Dec 1820. ??NYS -- described in Slocum, p. 60. Ch'i Ch'iao ch'u pien ho pi. After 1820. (Bibliothek Leiden 6891.) ??NYS (van der Waals). 476 examples. Nouveau Casse Tête Français. c1820 (according to van der Waals). Reproduced in van der Waals, but it's not clear how the pages are assembled. Milano dates it a c1815 and indicates it is 16 cards, but van der Waals looks like it may have been a booklet of 16 pp with TP, example page and end page. The 16 pp have 80 problems. Jerry Slocum has sent 2 large pages with 58 figurative shapes which are clearly the same pictures. The instructions are essentially the same, but are followed by rules for a Jeu de Patience on the second page and there is a 6 x 6 table of words on the first page headed "Morales trouvées dans les ruines de la célébres Ville de Persépolis ..." which one has to assemble into moral proverbs. It looks like these are copies of folding plates in some book of games. Chinese Puzzle Georgina. A. & S. Josh Myers, & Co 144, Leadenhall Street, London. Ganton Litho. 81 examples on 8 plates with elegant TP. Pages are one-sided sheets, sewn in the middle, but some are upside down. Seen at BL (1578/4938). Bestelmeier, 1823. Item 1278: Chinese Squares. It is not in the 1812 catalogue. Slocum. Compendium. Shows the above Bestelmeier entry. Anonymous. Ch'i ch'iao t'u ho pi (Harmoniously combined book of Tangram problems) and Ch'i ch'iao t'u chieh (Tangram solutions). Two volumes of tangrams and solutions with no title page, Chinese labels of the puzzles, in Chinese format (i.e. printed as long sheets on thin paper, accordion folded and stitched with ribbon. Nd [c1820s??], stiff card covers with flyleaves of a different paper, undoubtedly added later. 84 pages in each volume, containing 334 problems and solutions. With ownership stamp of a cartouche enclosing EWSHING, probably a Mr. E. W. Shing. Slocum says this is a c1820s reprint of the earliest Chinese tangram book which appeared in 1813 & 1815. This version omits the TP and opening text. I have a photocopy of the opening material from Slocum. The original problem book had a preface by Sang hsia K'o, which was repeated in the solution book with the same date. Includes all the problems of Shichi-kou-zu Gappeki, qv. New Series of Ch'i ch'iau puzzles. Printed by Lou Chen wan, Ch'uen Liang, January 1826. ??NYS. (Copy at Dept. of Oriental Studies, Durham Univ., cited in R. C. Bell; Tangram Teasers.) Neues chinesisches Rätselspiel für Kinder, in 24 bildlichen und alphabetischen Darstellungen. Friese, Pirna. Van der Waals, copying Santi, gives c1805, but Slocum, p. 60, reports that it first appears in Pirnaisches Wochenblatt of 19 Dec 1829, though there is another tangram in the issue of 16 Dec 1820. ??NYS. Child. Girl's Own Book. 1833: 85; 1839: 72; 1842: 156. "Chinese Puzzles -- These consist of pieces of wood in the form of squares, triangles, &c. The object is to arrange them so as to form various mathematical figures." Anon. Edo Chiekata (How to Learn It??) (In Japanese). Jan 1837, 19pp, 306 problems. (Unclear if this uses the Tangram pieces.) Reprinted in the same booklet as Sei Shōnagon, on pp. 37 55. A Grand Eastern Puzzle. C. Davenport & Co., London. Nd. ??NYS (van der Waals). (Dalgety has a copy and gives C. Davenporte (??SP) and Co., No. 20, Grafton Street, East Euston Square. Chinese pages dated 1813 in European binding with label bearing the above information.) Augustus De Morgan. On the foundations of algebra, No. 1. Transactions of the Cambridge Philosophical Society 7 (1842) 287-300. ??NX. On pp. 289, he says "the well-known toy called the Chinese Puzzle, in which a prescribed number of forms are given, and a large number of different arrangements, of which the outlines only are drawn, are to be produced." Crambrook. 1843. P. 4, no. 4: Chinese Puzzle. Chinese Books, thirteen numbers. Though not illustrated, this seems likely to be the Tangrams -- ?? Boy's Own Book. 1843 (Paris): 439. No. 19: The Chinese Puzzle. Instructions give five shapes and say to make one copy of some and two copies of the others. As written, this has two medium sized triangles instead of two large ones, though it is intended to be the tangrams. 11 problem shapes given, no answers. Most of the shapes occur in earlier tangram collections, particularly in A New Invented Chinese Puzzle. "The puzzle may be purchased, ..., at Mr. Wallis's, Skinner street, Snow hill, where numerous books, containing figures for this ingenious toy may also be obtained." = Boy's Treasury, 1844, pp. 426-427, no. 16. It is also reproduced, complete with the error, but without the reference to Wallis, as: de Savigny, 1846, pp. 355-356, no. 14: Le casse-tête chinois; Magician's Own Book, 1857, prob. 49, pp. 289-290; Landells, Boy's Own Toy-Maker, 1858, pp. 139-140; Book of 500 Puzzles, 1859, pp. 103 104; Boy's Own Conjuring Book, 1860, pp. 251-252; Wehman, New Book of 200 Puzzles, 1908, pp. 34 35. No. 20: The Circassian puzzle. "This is decidedly the most interesting puzzle ever invented; it is on the same principle, but composed of many more pieces than the Chinese puzzle, and may consequently be arranged in more intricate figures. ..." No pieces or problems are shown. In the next problem, it says: "This and the Circassian puzzle are published by Mr. Wallis, Skinner-street, Snow-hill." = Boy's Treasury, 1844, p. 427, no. 17. = de Savigny, 1846, p. 356, no. 15: Le problème circassien, but the next problem omits the reference to Wallis. Although I haven't recorded a Circassian puzzle yet -- cf in 6.S.2 -- I have just seen that the puzzle succeeding The Chinese Puzzle in Wehman, New Book of 200 Puzzles, 1908, pp. 35-36, is called The Puzzle of Fourteen which might be the Circassian puzzle. Taking a convenient size, this has two equilateral triangles of edge 1 and four each of the following: a 30o-60o-90o triangle with edges 2, 1, 3; a parallelogram with angles 60o and 120o with edges 1 and 2; a trapezium with base angles 60o and 60o, with lower and upper base edges 2 and 1, height 3/4 and slant edges 1/2 and 3/2. All 14 pieces make a rectangle 23 by 4. Yüklə 2,59 Mb. Dostları ilə paylaş:
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