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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
223:
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
163:
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
143:
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
151:
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
388:
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
293:
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
393:
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
236:
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,
233:
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.
148:
bear an uncanny resemblance to the playing pieces of the tangram and there were books dedicated to arranging them together to form pleasing patterns.
160:
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
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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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244:. Soon, tangram sets were being exported in great number from China, made of various materials, from glass, to wood, to tortoise shell.
187:
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".
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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.
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1436:. "Mathematical Games—on the Fanciful History and the Creative Challenges of the Puzzle Game of Tangrams",
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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
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1156:, by Barile, Margherita, From MathWorld – A Wolfram Web Resource, created by Eric W. Weisstein.
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172:. Nevertheless, it is generally believed that the puzzle was invented about 20 years earlier.
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789:"Calculation and measurement of center of mass: An all-in-one activity using Tangram puzzles"
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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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263:(The new Chinese Puzzle Game), consisted of 339 puzzles copied from
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on behalf of a number of Chinese scholars to the prominent puzzlist
1073:. United States Department Of The Treasury. 1890–1926. p. 1421
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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
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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
297:" an alternative title for the "Anchor Puzzle" sets.
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Turning Your Set of Tangram Into A Magic Math Puzzle
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1625:
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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.
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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:
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175:The prominent third-century mathematician
68:consisting of seven flat polygons, called
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1454:. New York: Simon & Schuster, 1961.
27:
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215:Reaching the Western world (1815–1820s)
1305:"How to Make a Classic Tangram Puzzle"
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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.
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1769:Mathematical manipulatives
1440:Aug. 1974, p. 98–103.
170:New Figures of the Tangram
18:
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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
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358:The Eighth Book of Tan
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265:The Eighth Book of Tan
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193:The Eighth Book Of Tan
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1784:Chinese ancient games
1413:Wereld vol spelletjes
1099:. BBC. Archived from
912:Hill, Thomas (1848).
860:. Jacobs. p. 315
409:(hypotenuse 1, sides
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257:Copenhagen University
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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
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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
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1406:
1403:
1402:0-399-22274-X
1399:
1395:
1394:0-698-11672-0
1391:
1387:
1386:0-399-21151-9
1383:
1379:
1375:
1374:
1370:
1364:
1358:
1354:
1349:
1345:
1339:
1335:
1330:
1329:
1325:
1324:
1310:
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1299:
1296:
1291:
1289:0-486-21483-4
1285:
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1266:
1262:
1258:
1254:
1250:
1246:
1245:
1237:
1234:
1231:, p. 37.
1230:
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1207:
1202:
1196:
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1188:
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1159:
1155:
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1136:
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1125:
1117:
1114:
1103:on 2011-10-02
1102:
1098:
1094:
1087:
1084:
1072:
1071:
1064:
1061:
1056:
1052:
1046:
1044:
1040:
1037:, p. 51.
1036:
1035:Slocum (2003)
1031:
1028:
1024:
1023:Slocum (2003)
1019:
1017:
1013:
1010:, p. 49.
1009:
1008:Slocum (2003)
1004:
1001:
998:, p. 31.
997:
996:Slocum (2003)
992:
989:
986:, p. 30.
985:
984:Slocum (2003)
980:
977:
974:, p. 15.
973:
972:Slocum (2003)
968:
965:
961:
960:Slocum (2003)
956:
953:
950:, p. 16.
949:
948:Slocum (2003)
944:
941:
938:, p. 25.
937:
936:Slocum (2003)
932:
929:
924:
917:
916:
908:
905:
902:, p. 23.
901:
900:Slocum (2003)
896:
894:
890:
887:
886:
881:
880:
874:
871:
859:
858:
850:
847:
843:
842:Slocum (2001)
838:
835:
830:
826:
822:
818:
814:
810:
806:
802:
798:
794:
790:
783:
780:
777:, p. 21.
776:
775:Slocum (2003)
771:
769:
765:
758:
754:
751:
749:
746:
744:
743:Tiling puzzle
741:
739:
736:
734:
731:
729:
726:
724:
722:
718:
717:
713:
707:
702:
697:
695:
693:
690:, and so its
689:
685:
608:
607:parallelogram
604:
564:
560:
504:
448:
408:
404:
403:
402:
396:
394:
392:
382:
375:
370:
365:
361:
359:
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347:
345:
337:
333:
330:
328:
327:Henry Dudeney
324:
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206:
205:Henry Dudeney
202:
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185:
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161:
159:
155:
149:
147:
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133:
131:
129:
128:
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119:
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108:
104:
96:
94:
92:
88:
84:
80:
75:
71:
67:
57:
51:
43:
39:
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26:
22:
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1704:
1694:
1473:
1466:
1451:
1444:
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1427:
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1408:
1377:
1355:. Sterling.
1352:
1333:
1312:. Retrieved
1308:
1298:
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1273:
1248:
1242:
1236:
1224:
1215:
1209:
1195:
1185:
1167:
1161:
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1138:. Retrieved
1123:
1116:
1105:. Retrieved
1101:the original
1096:
1086:
1075:. Retrieved
1069:
1063:
1054:
1030:
1003:
991:
979:
967:
955:
943:
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914:
907:
883:
877:
873:
862:. Retrieved
856:
849:
844:, p. 9.
837:
796:
792:
782:
723:(video game)
720:
692:mirror image
681:
646:, height of
400:
387:
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331:
316:
292:
281:
269:
264:
260:
252:
246:
241:
237:
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227:
208:
192:
191:in his 1908
186:
174:
169:
165:
162:
157:
154:feast tables
153:
150:
146:Song dynasty
142:
126:
117:
115:
110:
106:
102:
100:
73:
69:
53:
37:
35:
25:
1730:WikiProject
1638:Polydrafter
1612:Polyominoid
1548:Polyominoes
1465:Loyd, Sam.
1229:Slocum 2001
738:Ostomachion
288:earthenware
189:Samuel Loyd
122:Thomas Hill
91:World War I
1753:Categories
1690:Snake cube
1648:Polyiamond
1504:G. Sarcone
1314:2020-03-10
1140:2010-09-05
1107:2010-10-03
1077:2010-09-16
864:2010-10-13
799:(9): 652.
759:References
609:(sides of
317:A tangram
253:Mandarinen
1794:Polyforms
1685:Soma cube
1658:Polystick
1633:Polyabolo
1581:Heptomino
1571:Pentomino
1566:Tetromino
1540:Polyforms
829:251917733
821:0002-9505
686:but only
301:Paradoxes
97:Etymology
55:qīqiǎobǎn
1700:Hexastix
1617:Polycube
1596:Decomino
1591:Nonomino
1586:Octomino
1576:Hexomino
1396:(v. 2),
1388:(v. 1),
882:, 1910,
698:See also
521:, sides
470:, sides
405:2 large
360:(1903):
1706:Tantrix
1695:Tangram
1672:puzzles
1643:Polyhex
1561:Tromino
1404:(v. 3).
1326:Sources
1265:2303340
801:Bibcode
721:Tangram
676:
664:
662:, area
660:
648:
644:
631:√
627:
623:
611:
600:
588:
586:, area
584:
571:√
567:
565:(sides
556:
544:
542:, area
540:
527:√
523:
519:
507:
500:
488:
486:, area
484:
472:
468:
455:√
451:
444:
432:
430:, area
428:
415:√
411:
319:paradox
249:Denmark
199:editor
177:Liu Hui
139:Origins
134:History
83:America
42:Chinese
38:tangram
1740:Portal
1713:Tetris
1680:Blokus
1626:Others
1556:Domino
1480:
1458:
1419:
1400:
1392:
1384:
1359:
1340:
1286:
1263:
1131:
827:
819:
563:square
397:Pieces
391:convex
295:Sphinx
231:Trader
103:γράμμα
87:Europe
52::
50:pinyin
44::
1668:Games
1261:JSTOR
825:S2CID
323:monks
111:t'ang
79:China
1670:and
1478:ISBN
1456:ISBN
1417:ISBN
1398:ISBN
1390:ISBN
1382:ISBN
1357:ISBN
1338:ISBN
1284:ISBN
1129:ISBN
1097:h2g2
885:s.v.
817:ISSN
625:and
107:t'an
85:and
74:tans
70:tans
61:lit.
36:The
1253:doi
809:doi
242:Key
156:or
152:燕几(
46:七巧板
1755::
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494:/
491:1
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462:/
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446:)
441:4
438:/
435:1
425:2
422:/
417:2
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23:.
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