Knowledge (XXG)

Tangram

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923: 1735: 706: 350: 220: 306: 336: 381: 29: 1726: 346:(1903). Each of these cups was composed using the same seven geometric shapes. But the first cup is whole, and the others contain vacancies of different sizes. (Notice that the one on the left is slightly shorter than the other two. The one in the middle is ever-so-slightly wider than the one on the right, and the one on the left is narrower still.) 228:
The earliest extant tangram was given to the Philadelphia shipping magnate and congressman Francis Waln in 1802 but it was not until over a decade later that Western audiences, at large, would be exposed to the puzzle. In 1815, American Captain M. Donnaldson was given a pair of author Sang-Hsia-koi's
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A caricature published in France in 1818, when the tangram craze was at its peak. The caption reads: " 'Take care of yourself, you're not made of steel. The fire has almost gone out and it is winter.' 'It kept me busy all night. Excuse me, I will explain it to you. You play this game, which is said
124:. Hill likely coined the term in the same work, and vigorously promoted the word in numerous articles advocating for the puzzle's use in education, and in 1864 the word received official recognition in the English language when it was included in Noah Webster's 179:
made use of construction proofs in his works and some bear a striking resemblance to the subsequently developed banquet tables which in turn seem to anticipate the tangram. While there is no reason to suspect that tangrams were used in the proof of the
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According to Western sources, however, the tangram's historical Chinese inventor is unknown except through the pen name Yang-cho-chu-shih (Dim-witted (?) recluse, recluse = 处士). It is believed that the puzzle was originally introduced in a book titled
195:. This work contains many whimsical features that aroused both interest and suspicion amongst contemporary scholars who attempted to verify the account. By 1910 it was clear that it was a hoax. A letter dated from this year from the 76:
can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline. It is reputed to have been invented in
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Despite its relatively recent emergence in the West, there is a much older tradition of dissection amusements in China which likely played a role in its inspiration. In particular, the modular banquet tables of the
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Several Chinese sources broadly report a well-known Song dynasty polymath Huang Bosi 黄伯思 who developed a form of entertainment for his dinner guests based on creative arrangements of six small tables called 宴几 or
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Over 6500 different tangram problems have been created from 19th century texts alone, and the current number is ever-growing. Fu Traing Wang and Chuan-Chih Hsiung proved in 1942 that there are only thirteen
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More internationally, the First World War saw a great resurgence of interest in tangrams, on the homefront and trenches of both sides. During this time, it occasionally went under the name of "The
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tangram configurations (segments drawn between any two points on the configuration are always completely contained inside the configuration, i.e., configurations with no recesses in the outline).
72:, which are put together to form shapes. The objective is to replicate a pattern (given only an outline) generally found in a puzzle book using all seven pieces without overlap. Alternatively the 207:
reads "The result has been to show that the man Tan, the god Tan, and the Book of Tan are entirely unknown to Chinese literature, history or tradition." Along with its many strange details
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The puzzle eventually reached England, where it became very fashionable. The craze quickly spread to other European countries. This was mostly due to a pair of British tangram books,
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docked there. They were then brought with the ship to Philadelphia, in February 1816. The first tangram book to be published in America was based on the pair brought by Donnaldson.
329:, which consists of two similar shapes, one with and the other missing a foot. In reality, the area of the foot is compensated for in the second figure by a subtly larger body. 1476:. De Meern, Netherlands: Plenary Publications International (Europe); Amsterdam, Netherlands: ADM International; Seattle: Distributed by University of Washington Press, 1986. 184:, as is sometimes reported, it is likely that this style of geometric reasoning went on to exert an influence on Chinese cultural life that lead directly to the puzzle. 321:
is a dissection fallacy: Two figures composed with the same set of pieces, one of which seems to be a proper subset of the other. One famous paradox is that of the two
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Choosing a unit of measurement so that the seven pieces can be assembled to form a square of side one unit and having area one square unit, the seven pieces are:
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The seventh and eighth figures represent the mysterious square, built with seven pieces: then with a corner clipped off, and still the same seven pieces employed.
125: 93:. It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education. 313:
In figure 2, overlaying the bodies shows that footless body is larger by the foot's area. The change in area is often unnoticed as √2 is close to 1.5.
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bear an uncanny resemblance to the playing pieces of the tangram and there were books dedicated to arranging them together to form pleasing patterns.
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respectively). One diagram shows these as oblong rectangles, and other reports suggest a seventh table was added later, perhaps by a later inventor.
251:. Danish interest in tangrams skyrocketed around 1818, when two books on the puzzle were published, to much enthusiasm. The first of these was 1798: 1360: 1341: 1132: 101:
The origin of the English word 'tangram' is unclear. One conjecture holds that it is a compound of the Greek element '-gram' derived from
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The early years of attempting to date the Tangram were confused by the popular but fraudulently written history by famed puzzle maker
113:'Chinese'. Alternatively, the word may be derivative of the archaic English 'tangram' meaning "an odd, intricately contrived thing". 1481: 1459: 1420: 1401: 1393: 1385: 1287: 1243: 727: 1092: 369: 694:
can be obtained only by flipping it over. Thus, it is the only piece that may need to be flipped when forming certain shapes.
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to hail from China. And I tell you that what Paris needs right now is to welcome that which comes from far away.' "
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date of creation for the puzzle of 4000 years in antiquity had to be regarded as entirely baseless and false.
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forbade many forms of recreation on the sabbath, they made no objection to puzzle games such as the tangram.
1758: 1523: 1184: 283: 121: 1436:. "Mathematical Games—on the Fanciful History and the Creative Challenges of the Puzzle Game of Tangrams", 922: 1763: 1642: 915:
Puzzles to teach geometry : in seventeen cards numbered from the first to the seventeenth inclusive
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The eighth book of Tan – 700 Tangrams by Sam Loyd with an introduction and solutions by Peter Van Note
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by trading ships shortly after. It became very popular in Europe for a time, and then again during
219: 1793: 1739: 1516: 1260: 824: 711: 1200: 1156:, by Barile, Margherita, From MathWorld – A Wolfram Web Resource, created by Eric W. Weisstein. 1667: 1503: 1477: 1455: 1416: 1397: 1389: 1381: 1356: 1337: 1283: 1128: 816: 562: 305: 172:. Nevertheless, it is generally believed that the puzzle was invented about 20 years earlier. 65: 1494: 1050: 789:"Calculation and measurement of center of mass: An all-in-one activity using Tangram puzzles" 1652: 1252: 808: 752: 259:, which was a non-fictional work about the history and popularity of tangrams. The second, 41: 335: 271: 913: 116:
In either case, the first known use of the word is believed to be found in the 1848 book
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Campillo-Robles, Jose M.; Alonso, Ibon; Gondra, Ane; Gondra, Nerea (1 September 2022).
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One contributing factor in the popularity of the game in Europe was that although the
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The World of Games: Their Origins and History, How to Play Them, and How to Make Them
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Like most modern sets, this wooden tangram is stored in the square configuration.
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Fu Traing Wang; Chuan-Chih Hsiung (November 1942). "A Theorem on the Tangram".
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In figure 1, side lengths are labelled assuming the square has unit sides.
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The two-monks paradox – two similar shapes but one missing a foot:
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books on the subject (one problem and one solution book) when his ship,
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The 2nd Scientific American Book of Mathematical Puzzles and Diversions
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Of these seven pieces, the parallelogram is unique in that it has no
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Tangrams were first introduced to the German public by industrialist
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on behalf of a number of Chinese scholars to the prominent puzzlist
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Many of these unusual and exquisite tangram sets made their way to
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Sam Loyd's Book of Tangram Puzzles (The 8th Book of Tan Part I)
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The Magic Dice Cup tangram paradox – from Sam Loyd's book
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sometime around the late 18th century and then carried over to
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Past & Future: The Roots of Tangram and Its Developments
255:(About the Chinese Game). This was written by a student at 1018: 1016: 1070:
Treasury Decisions Under customs and other laws, Volume 25
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by mathematician and future Harvard University president
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Clipped square tangram paradox – from Loyd's book
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around 1891. The sets were made out of stone or false
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Turning Your Set of Tangram Into A Magic Math Puzzle
1666: 1625: 1604: 1546: 290:, and marketed under the name "The Anchor Puzzle". 1474:Puzzles of Old and New: How to Make and Solve Them 1051:"Tangram the incredible timeless 'Chinese' puzzle" 1380:(three volumes). New York: Philomel Books, 1987. 1179: 1177: 362: 1469:. Mineola, New York: Dover Publications, 1968. 918:. Boston : Wm. Crosby & H.P. Nichols. 1524: 384:The 13 convex shapes matched with tangram set 8: 1282:. New York: Dover Publications. p. 53. 1218:. New York: Dover Publications. p. 25. 59: 1531: 1517: 1509: 175:The prominent third-century mathematician 68:consisting of seven flat polygons, called 1045: 1043: 1454:. New York: Simon & Schuster, 1961. 27: 764: 215:Reaching the Western world (1815–1820s) 1305:"How to Make a Classic Tangram Puzzle" 1228: 1034: 1022: 1007: 995: 983: 971: 959: 947: 935: 899: 841: 774: 748:Pickagram (3D Magnetic Tangram Puzzle) 240:, and the accompanying solution book, 64:'seven boards of skill') is a 1443:Gardner, Martin. "More on Tangrams", 1430:. New York: Dover Publications, 1958. 309:Explanation of the two-monks paradox: 7: 1303:Brooks, David J. (1 December 2018). 505:2 small right triangles (hypotenuse 449:1 medium right triangle (hypotenuse 278:Second craze in Germany (1891–1920s) 1725: 1189:. 1903 – via Tangram Channel. 1127:. John Wiley and Sons. p. 10. 1415:). New York: Facts on File, 1989. 14: 1244:The American Mathematical Monthly 1733: 1724: 921: 854:Forbrush, William Byron (1914). 728:Egg of Columbus (tangram puzzle) 704: 118:Geometrical Puzzle for the Young 1186:The 8th Book of Tan by Sam Loyd 1170:. New York: Dover Publications. 1093:"Tangram – The Chinese Puzzle" 238:The Fashionable Chinese Puzzle 54: 1: 1799:19th-century fads and trends 261:Det nye chinesiske Gaadespil 1447:Sep. 1974, p. 187–191. 1280:Tangrams : 330 Puzzles 1124:Kids Around The World Play! 793:American Journal of Physics 267:, as well as one original. 1815: 1769:Mathematical manipulatives 1440:Aug. 1974, p. 98–103. 170:New Figures of the Tangram 18: 1722: 1428:Amusements in Mathematics 1168:Amusements in Mathematics 879:Oxford English Dictionary 109:'to extend' or Cantonese 45: 1407:Botermans, Jack, et al. 1278:Read, Ronald C. (1965). 1121:Braman, Arlette (2002). 376:Number of configurations 209:The Eighth Book of Tan's 21:Tangram (disambiguation) 1091:Wyatt (26 April 2006). 284:Friedrich Adolf Richter 1472:Slocum, Jerry, et al. 1351:Slocum, Jerry (2003). 1336:. Barnes & Noble. 1332:Slocum, Jerry (2001). 1055:www.archimedes-lab.org 385: 372: 366: 358:The Eighth Book of Tan 353: 339: 314: 265:The Eighth Book of Tan 225: 193:The Eighth Book Of Tan 33: 1784:Chinese ancient games 1413:Wereld vol spelletjes 1099:. BBC. Archived from 912:Hill, Thomas (1848). 860:. Jacobs. p. 315 409:(hypotenuse 1, sides 383: 371: 352: 338: 308: 257:Copenhagen University 222: 31: 1779:Geometric dissection 1201:"The Magic Dice Cup" 1166:Dudeney, H. (1958). 19:For other uses, see 1774:Single-player games 1502:by puzzle designer 1445:Scientific American 1438:Scientific American 1309:Boys' Life magazine 805:2022AmJPh..90..652C 733:Mathematical puzzle 688:rotational symmetry 684:reflection symmetry 344:The 8th Book of Tan 182:Pythagorean theorem 127:American Dictionary 1789:Chinese inventions 1334:The Tao of Tangram 1214:Loyd, Sam (1968). 1025:, pp. 99–100. 712:Mathematics portal 386: 373: 354: 340: 315: 226: 34: 1746: 1745: 1605:Higher dimensions 1450:Gardner, Martin. 1378:Anno's Math Games 1376:Anno, Mitsumasa. 1362:978-1-4027-0413-0 1343:978-1-4351-0156-2 1134:978-0-471-40984-7 962:, pp. 16–19. 813:10.1119/5.0061884 197:Oxford Dictionary 66:dissection puzzle 62: 16:Dissection puzzle 1806: 1738: 1737: 1728: 1727: 1653:Pseudo-polyomino 1533: 1526: 1519: 1510: 1426:Dudeney, H. E. 1411:(translation of 1366: 1353:The Tangram Book 1347: 1319: 1318: 1316: 1315: 1300: 1294: 1293: 1275: 1269: 1268: 1238: 1232: 1226: 1220: 1219: 1211: 1205: 1204: 1197: 1191: 1190: 1181: 1172: 1171: 1163: 1157: 1151: 1145: 1144: 1142: 1141: 1118: 1112: 1111: 1109: 1108: 1088: 1082: 1081: 1079: 1078: 1065: 1059: 1058: 1047: 1038: 1032: 1026: 1020: 1011: 1005: 999: 993: 987: 981: 975: 969: 963: 957: 951: 945: 939: 933: 927: 926: 925: 919: 909: 903: 897: 888: 875: 869: 868: 866: 865: 851: 845: 839: 833: 832: 784: 778: 772: 753:Attribute blocks 714: 709: 708: 677: 675: 674: 671: 668: 661: 659: 658: 655: 652: 645: 643: 642: 639: 636: 635: 634: 624: 622: 621: 618: 615: 601: 599: 598: 595: 592: 585: 583: 582: 579: 576: 575: 574: 557: 555: 554: 551: 548: 541: 539: 538: 535: 532: 531: 530: 520: 518: 517: 514: 511: 501: 499: 498: 495: 492: 485: 483: 482: 479: 476: 469: 467: 466: 463: 460: 459: 458: 445: 443: 442: 439: 436: 429: 427: 426: 423: 420: 419: 418: 325:, attributed to 201:Sir James Murray 166:Ch'i chi'iao t'u 63: 60: 56: 47: 1814: 1813: 1809: 1808: 1807: 1805: 1804: 1803: 1749: 1748: 1747: 1742: 1732: 1718: 1662: 1621: 1600: 1542: 1537: 1491: 1434:Gardner, Martin 1373: 1371:Further reading 1363: 1350: 1344: 1331: 1323: 1322: 1313: 1311: 1302: 1301: 1297: 1290: 1277: 1276: 1272: 1257:10.2307/2303340 1240: 1239: 1235: 1227: 1223: 1213: 1212: 1208: 1203:. 2 April 2011. 1199: 1198: 1194: 1183: 1182: 1175: 1165: 1164: 1160: 1154:Tangram Paradox 1152: 1148: 1139: 1137: 1135: 1120: 1119: 1115: 1106: 1104: 1090: 1089: 1085: 1076: 1074: 1067: 1066: 1062: 1049: 1048: 1041: 1033: 1029: 1021: 1014: 1006: 1002: 994: 990: 982: 978: 970: 966: 958: 954: 946: 942: 934: 930: 920: 911: 910: 906: 898: 891: 876: 872: 863: 861: 853: 852: 848: 840: 836: 786: 785: 781: 773: 766: 761: 710: 703: 700: 672: 669: 666: 665: 663: 656: 653: 650: 649: 647: 640: 637: 632: 630: 629: 628: 626: 619: 616: 613: 612: 610: 596: 593: 590: 589: 587: 580: 577: 572: 570: 569: 568: 566: 552: 549: 546: 545: 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Index

Tangram (disambiguation)

Chinese
pinyin
dissection puzzle
China
America
Europe
World War I
Thomas Hill
American Dictionary
Song dynasty
Liu Hui
Pythagorean theorem
Samuel Loyd
Oxford Dictionary
Sir James Murray
Henry Dudeney

Denmark
Copenhagen University
Catholic Church
Friedrich Adolf Richter
earthenware
Sphinx

paradox
monks
Henry Dudeney

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