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In the simplest case, we are given a set of points S in the plane, which are the
Voronoi sites. Each site s has a Voronoi cell V(s) consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to two sites. The
366:
The Venn diagram is constructed with a collection of simple closed curves drawn in the plane. The principle of these diagrams is that classes be represented by regions in such relation to one another that all the possible logical relations of these classes can be indicated in the same diagram. That
337:
At each crossing we must indicate which section is "over" and which is "under", so as to be able to recreate the original knot. This is often done by creating a break in the strand going underneath. If by following the diagram the knot alternately crosses itself "over" and "under", then the diagram
304:
x, or y is an immediate successor of x. In a Hasse diagram, it is required that the curves be drawn so that each meets exactly two vertices: its two endpoints. Any such diagram (given that the vertices are labeled) uniquely determines a partial order, and any partial order has a unique transitive
362:
is a representation of mathematical sets: a mathematical diagram representing sets as circles, with their relationships to each other expressed through their overlapping positions, so that all possible relationships between the sets are shown.
165:(DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name "butterfly" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the
463:. Wallpaper groups categorize patterns by their symmetries. Subtle differences may place similar patterns in different groups, while patterns which are very different in style, color, scale or orientation may belong to the same group.
439:
is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct
325:
a useful way to visualise and manipulate knots is to project the knot onto a plane—;think of the knot casting a shadow on the wall. A small perturbation in the choice of projection will ensure that it is
367:
is, the diagram initially leaves room for any possible relation of the classes, and the actual or given relation, can then be specified by indicating that some particular region is null or is not null.
483:, is a finite collection of boxes, or cells, arranged in left-justified rows, with the row sizes weakly decreasing (each row has the same or shorter length than its predecessor).
305:
reduction, but there are many possible placements of elements in the plane, resulting in different Hasse diagrams for a given order that may have widely varying appearances.
567:
539:
515:
907:
Puphaiboon, K.; Woodcock, A.; Scrivener, S. (25 March 2005). "Design method for developing mathematical diagrams". In Bust, Philip D.; McCabe, P.T. (eds.).
1651:
233:, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
1322:
719:: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental Functions
1292:
137:
of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.
780:
772:
1621:
890:
Mathematical knowledge management: third international conference, MKM 2004, Białowieża, Poland, September 19–21, 2004 : Proceedings
968:
268:. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from
1001:
541:, and it carries the same information as that partition. Listing the number of boxes in each column gives another partition, the
839:
Barker-Plummer, Dave; Bailin, Sidney C. (2001). "On the practical semantics of mathematical diagrams". In
Anderson, M. (ed.).
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897:
862:
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726:
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Kidman, G. (2002). "The
Accuracy of mathematical diagrams in curriculum materials". In Cockburn, A.; Nardi, E. (eds.).
949:
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909:
Contemporary ergonomics 2005 Proceedings of the
International Conference on Contemporary Ergonomics (CE2005)
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569:; one obtains a Young diagram of that shape by reflecting the original diagram along its main diagonal.
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86:(1768–1822), although they were first described by Norwegian-Danish land surveyor and mathematician
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1080:
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Wessel's memoir was presented to the Danish
Academy in 1797; Argand's paper was published in 1806.
581:
91:
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1208:
1095:
987:
848:
824:
815:
Barker-Plummer, Dave; Bailin, Sidney C. (1997). "The Role of
Diagrams in Mathematical Proofs".
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154:
41:, are mainly designed to convey mathematical relationships—for example, comparisons over time.
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can be visually represented as a pair of numbers forming a vector on a diagram called an
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determined by distances to a specified discrete set of objects in the space, e.g., by a
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Commutative diagrams play the role in category theory that equations play in algebra.
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90:(1745–1818). Argand diagrams are frequently used to plot the positions of the
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is a portion of the computation that combines the results of smaller
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in 1903. Their theory was further developed by many mathematicians.
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888:. In Andréa Asperti; Bancerek, Grzegorz; Trybulec, Andrzej (eds.).
230:
110:
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Voronoi nodes are the points equidistant to three (or more) sites
334:, where the "shadow" of the knot crosses itself once transversely
1626:
1138:
779:, Encarta World English Dictionary, North American Edition 2007.
308:
184:
that depend on them (right) for a "butterfly" step of a radix-2
140:
969:"Diagrams in Mathematical Education: A Philosophical Appraisal"
169:, used for finding the most likely sequence of hidden states.
1133:
835:(Special Issue on Diagrammatic Representation and Reasoning).
403:, a Voronoi decomposition, or a Dirichlet tessellation after
34:
1009:
886:"On Diagrammatic Representation of Mathematical Knowledge"
199:
44:
1158:
876:. Vol. 3. University of East Anglia. pp. 201–8.
121:
of two complex numbers can be expressed most easily in
338:
represents a particularly well-studied class of knot,
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527:
503:
838:
814:
801:. Republished in part by Dover in 1960. p. 157.
16:
Visual representation of a mathematical relationship
950:"Diagrammatics: The art of thinking with diagrams"
561:
533:
509:
971:. Philosophy of Education Society. Archived from
451:, intermediate in complexity between the simpler
1873:
494:Listing the number of boxes in each row gives a
714:Whittaker, Edmund Taylor; Watson, G.N. (1927).
713:
176:show a data-flow diagram connecting the inputs
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995:
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961:One of the oldest extant diagrams from Euclid
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841:Reasoning with Diagrammatic Representations
422:
1002:
988:
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105:The concept of the complex plane allows a
852:
828:
721:. Cambridge University Press. p. 9.
129:of the product is the product of the two
109:interpretation of complex numbers. Under
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387:is a special kind of decomposition of a
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344:
307:
238:
225:, a commutative diagram is a diagram of
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18:
938:The Stanford Encyclopedia of Philosophy
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395:of points. This diagram is named after
45:Specific types of mathematical diagrams
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210:
196:shown for comparison, hence the name.
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447:Wallpaper groups are two-dimensional
330:except at the double points, called
203:A commutative diagram depicting the
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13:
808:
572:Young tableaux were introduced by
378:
221:In mathematics, and especially in
14:
1898:
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256:is a simple picture of a finite
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892:. Springer. pp. 191–204.
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405:Peter Gustav Lejeune Dirichlet
229:, also known as vertices, and
133:, or moduli, and the angle or
26:, ms. from LĂĽneburg, A.D. 1200
1:
1026:Biological data visualization
685:
437:plane crystallographic group
7:
817:Machine Graphics and Vision
717:A Course of Modern Analysis
643:
592:Other mathematical diagrams
188:. This diagram resembles a
163:discrete Fourier transforms
10:
1905:
1066:Mathematical visualization
798:A Survey of Symbolic Logic
675:Mathematical visualization
455:and the three-dimensional
214:
186:Cooley–Tukey FFT algorithm
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1061:Information visualization
1046:Educational visualization
1018:
874:Proceedings of the PME 26
670:Mathematics as a language
300:. In this case, we say y
1237:Charles-René de Fourcroy
1086:Scientific visualization
1013:of technical information
911:. Taylor & Francis.
562:{\displaystyle \lambda }
534:{\displaystyle \lambda }
510:{\displaystyle \lambda }
423:Wallpaper group diagrams
418:Wallpaper group diagram.
399:, also called a Voronoi
82:. These are named after
74:is sometimes called the
457:crystallographic groups
264:of the partial order's
1657:Christopher R. Johnson
1209:Technical illustration
1096:Software visualization
967:Lomas, Dennis (1998).
743:Rolfsen, Dale (1976).
563:
535:
517:of a positive integer
511:
491:
419:
375:
350:
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244:
207:
180:(left) to the outputs
155:fast Fourier transform
145:
102:in the complex plane.
78:because it is used in
59:
27:
1887:Mathematical concepts
1551:Lawrence J. Rosenblum
1364:Edward Walter Maunder
1288:Charles Joseph Minard
1106:User interface design
1081:Product visualization
793:Clarence Irving Lewis
749:. Publish or Perish.
699:Working with diagrams
564:
536:
512:
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373:
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311:
258:partially ordered set
242:
202:
143:
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31:Mathematical diagrams
22:
1831:Scientific modelling
1806:Information graphics
1546:Clifford A. Pickover
1496:William S. Cleveland
1404:Henry Norris Russell
1389:Howard G. Funkhouser
1333:Florence Nightingale
1298:Francis Amasa Walker
1194:Statistical graphics
1116:Volume visualization
1091:Social visualization
582:Cambridge University
553:
525:
501:
433:plane symmetry group
374:Voronoi centerlines.
266:transitive reduction
1811:Information science
1774:in computer science
1566:Sheelagh Carpendale
1501:George G. Robertson
1338:Karl Wilhelm Pohlke
1273:André-Michel Guerry
1149:Graph of a function
1144:Engineering drawing
660:Mathematical jargon
217:Commutative diagram
211:Commutative diagram
125:— the magnitude or
1851:Volume cartography
1615:Early 21st century
1511:Catherine Plaisant
1506:Bruce H. McCormick
1460:Mary Eleanor Spear
1450:Arthur H. Robinson
1384:Arthur Lyon Bowley
1357:Early 20th century
1204:Technical drawings
1076:Molecular graphics
1051:Flow visualization
1041:Data visualization
963:by Otto Neugebauer
956:on April 25, 2013.
775:2009-11-07 at the
665:Mathematical model
633:Van Kampen diagram
623:Stellation diagram
613:Elementary diagram
603:De Finetti diagram
559:
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507:
492:
420:
376:
351:
314:
245:
208:
153:In the context of
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84:Jean-Robert Argand
60:
28:
1869:
1868:
1846:Visual perception
1796:Graphic organizer
1769:Computer graphics
1740:
1739:
1722:Martin Wattenberg
1697:Hanspeter Pfister
1652:Martin Krzywinski
1576:Jock D. Mackinlay
1556:Thomas A. DeFanti
1479:Late 20th century
1399:Ejnar Hertzsprung
1101:Technical drawing
918:978-0-415-37448-4
899:978-3-540-23029-8
864:978-1-85233-242-6
756:978-0-914098-16-4
728:978-0-521-58807-2
701:at LearningSpace.
680:Statistical model
340:alternating knots
174:butterfly diagram
167:Viterbi algorithm
149:Butterfly diagram
144:Butterfly diagram
123:polar coordinates
24:Euclid's Elements
1894:
1856:Volume rendering
1841:Visual analytics
1836:Spatial analysis
1816:Misleading graph
1667:David McCandless
1642:Gordon Kindlmann
1606:Alfred Inselberg
1601:Leland Wilkinson
1536:Michael Friendly
1470:Howard T. Fisher
1433:Mid 20th century
1374:W. E. B. Du Bois
1278:William Playfair
1268:Adolphe Quetelet
1242:Joseph Priestley
1225:Pre-19th century
1222:
1221:
1189:Skeletal formula
1056:Geovisualization
1031:Chemical imaging
1004:
997:
990:
981:
980:
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952:. Archived from
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284:and there is no
194:Morpho butterfly
113:, they add like
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1861:Information art
1801:Imaging science
1746:
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1717:Fernanda Viégas
1712:Moritz Stefaner
1637:Jessica Hullman
1610:
1581:Alan MacEachren
1531:Ben Shneiderman
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1071:Medical imaging
1014:
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845:Springer Verlag
811:
809:Further reading
806:
805:
791:
787:
777:Wayback Machine
768:
764:
757:
746:Knots and links
741:
737:
729:
711:
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705:
697:
693:
688:
650:Category theory
646:
598:Cremona diagram
594:
586:Georg Frobenius
554:
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481:Ferrers diagram
469:
449:symmetry groups
429:wallpaper group
425:
385:Voronoi diagram
381:
379:Voronoi diagram
356:
319:
276:precisely when
250:
223:category theory
219:
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151:
131:absolute values
80:Argand diagrams
58:Argand diagram.
52:
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975:on 2011-07-21.
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927:External links
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854:10.1.1.30.9246
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830:10.1.1.49.4712
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770:"Venn diagram"
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608:Dynkin diagram
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490:Young diagram.
479:, also called
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459:, also called
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397:Georgy Voronoi
380:
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318:
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249:
248:Hasse diagrams
246:
243:Hasse diagram.
215:Main article:
212:
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157:algorithms, a
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119:multiplication
68:Argand diagram
64:complex number
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50:Argand diagram
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1542:
1541:Howard Wainer
1539:
1537:
1534:
1532:
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1483:
1481:
1477:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1445:Rudolf Modley
1443:
1441:
1438:
1437:
1435:
1431:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1409:Max O. Lorenz
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1361:
1359:
1355:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1329:
1326:
1324:
1321:
1319:
1318:Charles Booth
1316:
1314:
1311:
1309:
1306:
1304:
1301:
1299:
1296:
1294:
1293:Luigi Perozzo
1291:
1289:
1286:
1284:
1283:August Kekulé
1281:
1279:
1276:
1274:
1271:
1269:
1266:
1264:
1263:Charles Dupin
1261:
1260:
1258:
1254:
1248:
1247:Gaspard Monge
1245:
1243:
1240:
1238:
1235:
1233:
1232:Edmond Halley
1230:
1229:
1227:
1223:
1220:
1216:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1182:
1180:
1177:
1175:
1172:
1170:
1167:
1165:
1162:
1160:
1157:
1155:
1152:
1150:
1147:
1145:
1142:
1140:
1137:
1135:
1132:
1131:
1129:
1123:
1117:
1114:
1112:
1109:
1107:
1104:
1102:
1099:
1097:
1094:
1092:
1089:
1087:
1084:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1036:Crime mapping
1034:
1032:
1029:
1027:
1024:
1023:
1021:
1017:
1012:
1011:Visualization
1005:
1000:
998:
993:
991:
986:
985:
982:
974:
970:
965:
962:
959:
955:
951:
947:
943:
939:
935:
931:
930:
920:
914:
910:
905:
901:
895:
891:
887:
883:
879:
875:
870:
866:
860:
855:
850:
846:
842:
837:
831:
826:
822:
818:
813:
812:
800:
799:
794:
789:
782:
778:
774:
771:
766:
758:
752:
748:
747:
739:
730:
724:
720:
718:
707:
700:
695:
691:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
655:Logic diagram
653:
651:
648:
647:
639:
636:
634:
631:
629:
626:
624:
621:
619:
618:Euler diagram
616:
614:
611:
609:
606:
604:
601:
599:
596:
595:
589:
587:
583:
579:
578:mathematician
575:
570:
556:
549:partition of
548:
544:
528:
520:
504:
497:
488:
484:
482:
478:
477:Young tableau
474:
473:Young diagram
467:Young diagram
464:
462:
458:
454:
453:frieze groups
450:
445:
443:
438:
434:
430:
416:
412:
408:
406:
402:
398:
394:
390:
386:
372:
368:
364:
361:
349:Venn diagram.
347:
343:
341:
335:
333:
329:
324:
317:Knot diagrams
312:Knot diagram.
310:
306:
303:
299:
295:
291:
287:
283:
279:
275:
271:
267:
263:
259:
255:
254:Hasse diagram
241:
237:
234:
232:
228:
224:
218:
206:
201:
197:
195:
191:
187:
183:
179:
175:
170:
168:
164:
160:
156:
142:
138:
136:
132:
128:
124:
120:
116:
112:
108:
103:
101:
97:
93:
89:
88:Caspar Wessel
85:
81:
77:
73:
72:complex plane
69:
65:
56:
42:
40:
36:
32:
25:
21:
1821:Neuroimaging
1781:CPK coloring
1764:Color coding
1702:Hans Rosling
1682:Miriah Meyer
1647:Aaron Koblin
1632:Jeffrey Heer
1526:Edward Tufte
1521:Pat Hanrahan
1491:Nigel Holmes
1369:Otto Neurath
1308:Oliver Byrne
1256:19th century
1065:
973:the original
954:the original
946:Kulpa, Zenon
940:. Fall 2008.
937:
908:
889:
882:Kulpa, Zenon
873:
840:
823:(1): 25–56.
820:
816:
797:
788:
765:
745:
738:
715:
706:
694:
574:Alfred Young
571:
546:
542:
518:
493:
472:
470:
461:space groups
446:
436:
432:
426:
409:
401:tessellation
393:discrete set
389:metric space
382:
365:
360:Venn diagram
357:
354:Venn diagram
336:
331:
320:
297:
293:
289:
285:
281:
277:
273:
269:
260:, forming a
251:
235:
220:
181:
177:
171:
152:
134:
126:
104:
79:
76:Argand plane
75:
61:
30:
29:
1754:Cartography
1692:Ade Olufeko
1662:Manuel Lima
1591:Kwan-Liu Ma
1516:Stuart Card
1486:Borden Dent
1424:Erwin Raisz
1379:Henry Gantt
783:2009-11-01.
628:Ulam spiral
323:Knot theory
1876:Categories
1677:John Maeda
1455:John Tukey
1419:Harry Beck
1414:Fritz Kahn
1164:Photograph
934:"Diagrams"
686:References
328:one-to-one
288:such that
205:five lemma
192:as in the
33:, such as
1759:Chartjunk
1727:Bang Wong
1622:Polo Chau
1328:John Snow
1303:John Venn
1184:Schematic
1169:Pictogram
849:CiteSeerX
825:CiteSeerX
557:λ
547:transpose
543:conjugate
529:λ
505:λ
496:partition
332:crossings
231:morphisms
190:butterfly
159:butterfly
107:geometric
1882:Diagrams
1745:Related
1154:Ideogram
884:(2004).
795:(1918).
781:Archived
773:Archived
644:See also
135:argument
111:addition
100:function
1627:Ben Fry
1139:Diagram
262:drawing
227:objects
127:modulus
115:vectors
1747:topics
1218:People
1125:Image
1019:Fields
915:
896:
861:
851:
827:
753:
725:
442:groups
302:covers
117:. The
96:zeroes
39:graphs
35:charts
1199:Table
1134:Chart
1127:types
296:<
292:<
280:<
98:of a
92:poles
1174:Plot
913:ISBN
894:ISBN
859:ISBN
751:ISBN
723:ISBN
576:, a
172:The
94:and
70:The
37:and
1159:Map
580:at
545:or
475:or
435:or
431:or
321:In
272:to
1878::
948:.
936:.
857:.
847:.
843:.
819:.
471:A
444:.
427:A
407:.
383:A
358:A
342:.
252:A
62:A
1003:e
996:t
989:v
921:.
902:.
867:.
833:.
821:6
759:.
733:)
731:.
712:(
519:n
298:y
294:z
290:x
286:z
282:y
278:x
274:y
270:x
182:y
178:x
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