1367:
surface, assuming that the gluing is performed in the 3D space, rather than through some topological magic (sorry, I am not an expert in this field and lack the right terminology; my judgements are restricted to common sense intuition). Note that the article about the umbilic torus doesn't establish any relation of it with the Möbius strip (the link in the "See also" section doesn't count as such). I think that the misleading sentence has to be either removed or reformulated in a less confusing way and a more detailed explanation can be provided in the article about umbilic torus.
786:
474:
464:
443:
1405:. My feeling was that something was wrong with it. A Möbius strip is single-sided whereas the Umbilic torus apparently has inside and outside. Now thinking about it more carefully, I guess that I found the flaw in your reasoning. The fact that the boundary goes three times around the center of the torus doesn't mean that the strip makes three half-twists. Actually it only makes a full twist (two half-twists). Hence it is not topologically equivalent to a Möbius strip.
1117:
the main point of a movie about this character, then maybe it could be listed among other fictional works with Möbius-strip plotlines. Or if your links' theory that this is another example of the bullshit "Möbius strips are things we don't understand therefore they could cause time loops" trope turns out to be validated, then maybe it could be mentioned, briefly, in the sentence with three examples of this trope. But the current
Knowledge article
555:
917:
21:
1122:
to which the idea of a Möbius strip has had a significant influence (fine art, design, literature, etc). A name of a character in a movie franchise is not a significant influence to a wide area of popular culture. We already have plenty of examples of movies where the strip plays a much more significant role in the overall structure of the movie and not just in the names or behavior of one its characters. —
412:
1001:
381:
126:
877:
750:
1204:
couldn't find anything, which is a crude way of going about things, but I'd find it highly unlikely that someone would evaluate the area analytically and not put a numerical value to it. So I suspect it's not been properly investigated, and I doubt there's a closed form. For posterity, the integral is
1382:
You are confusing the standard embedding of the Möbius strip (with one half-twist) with the Möbius strip itself (a topological surface independent of how it is embedded into space). If you perform any odd number of half-twists to a strip before gluing it back to itself, you get a Möbius strip, with a
1121:
contains no content that would make a significant enough connection to this article to link to. The popular culture section is not intended as a catch-all listing of anything vaguely related (go to tvtropes for that sort of thing), but as an organized survey of different wide areas of popular culture
1116:
I'm leaning towards no. If the connection is only to the misspelled name "Mobius", no. If we have in-depth published reliable sources specifically connecting this character's plot line to the Möbius strip itself, and not just fan speculation which some of your sources look like, and this plot line is
1366:
The link to "Umbilic torus" in the "See also" section is accompanied with a claim that the
Umbilic torus can be obtained from a Möbius strip by gluing the latter along its single edge. IMHO, that statement is false, at least in regular 3D space, where the result would have to be a self-intersecting
1004:
Article has achieved Good
Article status. No issues of copyvio or plagiarism. All sources appear reliable. QPQ is done. Hooks are interesting and sourced. Are there any other images you would like to include in the nomination? There are some cool ones in commons, but I guess new hooks would have to
1203:
Interesting. Numerically (from their formula) it's ≈6.62715 for a fairly natural choice of dimensions, namely a strip width of 1 unit rotating while following a circle of radius 1, indeed slightly greater than Pappus's theorem's estimate of 2π. I searched for that constant (and approximations) and
1383:
different embedding for each different number of half-twists (see the second paragraph of the lead). The umbilic torus has a boundary that, if you cut along the ridges, is a Möbius strip. It is a Möbius strip embedded with three half-twists rather than one, but that is still a Möbius strip. —
1419:
Ok, this time I think you may be correct. If it really were a Möbius strip then (regardless of number of twists) traveling around the boundary (without crossing any ridges) until you return to your start should take you to the inside, but it doesn't.
617:
Wouldn't that create two Möbius strips instead? Explanation caption for the image lists that it creates a Möbius strip with two tracks, and one non Möbius strip. In reality, this should create a two tracked Möbius strip and a separate Möbius strip.
1344:
1142:
It might be interesting to say what the area of the surface swept by a rotating line segment is. I don't know the answer, but I found a reference saying what the area isn't: it isn't what you would get by trying to apply
327:
1458:
973:
653:
As for ALT1 below. Aion is NOT holding a Möbius strip. Give me a break and take a better look. It is just a strip and the Romans perished (due to lead poisoning) before even inventing zero.
530:
321:
372:
1047:
Promoter comment: taking the recycling logo because I can image lots of people will be trying to work it out and surprised to learn because that logo is so commonplace.
733:
134:
660:
1207:
1468:
520:
253:
1097:
218:
1463:
496:
259:
785:
857:
151:
50:
32:
1453:
1154:
487:
448:
1448:
865:
342:
273:
204:
38:
309:
278:
194:
572:
568:
368:
364:
916:
876:
664:
248:
423:
692:
602:
239:
1144:
1089:
380:
359:
303:
581:
391:
1425:
1388:
1193:
1127:
1024:
987:
299:
109:
90:
1093:
1019:
I added three more for some of the other hooks. Not sure the mosaic one works at DYK thumbnail size though. —
1410:
1372:
283:
623:
1147:. The rotation makes it sweep out a bigger area than a non-rotating segment would. See the last line of:
349:
1406:
1368:
429:
144:
20:
858:
https://www.npr.org/sections/thesalt/2015/08/06/429437860/cut-your-bagel-the-mathematically-correct-way
473:
1085:
1081:
656:
619:
1421:
1384:
1189:
1123:
1020:
983:
335:
229:
125:
495:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
1171:
587:
479:
396:
244:
861:
749:
463:
442:
315:
1052:
1038:
1010:
713:
638:
225:
42:
945:
866:
https://www.nytimes.com/2012/01/10/science/pasta-inspires-scientists-to-use-their-noodle.html
776:
1351:
1339:{\displaystyle \int _{0}^{2\pi }\int _{0}^{1}{\sqrt {(t/2)^{2}+(1+t\cos(s/2))^{2}}}\,dt\,ds}
1163:
1118:
1106:
1075:
761:
583:
554:
393:
161:
1181:
1178:
956:
934:
894:
850:
832:
806:
769:
198:
169:
1442:
677:
The following is an archived discussion of the DYK nomination of the article below.
1167:
1152:
Goodman, A. W.; Goodman, Gary (1969), "Generalizations of the theorems of Pappus",
1048:
1034:
1006:
790:
709:
634:
1033:
You are right, the mosaic wouldn't work. Shame about that. The others look good.
1347:
1102:
492:
1000:
683:
Subsequent comments should be made on the appropriate discussion page (such as
469:
138:
1429:
1414:
1392:
1376:
1355:
1197:
1131:
1110:
1056:
1042:
1028:
1014:
991:
717:
668:
642:
627:
839:
830:: ... that Parisian seamstresses initiated novices by making them sew a
817:
585:
395:
1174:
963:
695:), unless there is consensus to re-open the discussion at this page.
821:
974:
Template:Did you know nominations/Frequency modulation encoding
905:
633:
The pink/blue strip has two sides and is not a Möbiusstrip. --
588:
548:
405:
397:
189:
862:
https://www.theverge.com/2014/9/5/6110563/mobius-bacon-recipe
946:
https://books.google.com/books?id=IwDvAAAAMAAJ&pg=PA53
777:
https://books.google.com/books?id=RMH2DwAAQBAJ&pg=PA31
1402:
1398:
738:
729:
102:
83:
1459:
Knowledge Did you know articles that are good articles
334:
1210:
491:, a collaborative effort to improve the coverage of
1338:
898:can be made to have a perfectly circular boundary
938:stays in one piece when cut along its centerline
854:has been used to shape bagels, bacon, and pasta?
207:for general discussion of the article's subject.
48:If it no longer meets these criteria, you can
596:This page has archives. Sections older than
348:
8:
1078:be included in the popular culture section?
960:can have two sides in non-Euclidean spaces?
697:No further edits should be made to this page
654:
437:
62:
15:
1312:
1297:
1264:
1252:
1244:
1238:
1233:
1220:
1215:
1209:
1397:You provided the same justification in
1328:
1320:
439:
606:when more than 5 sections are present.
921:Möbius strip cut along its centerline
881:Möbius strip with a circular boundary
840:https://www.jstor.org/stable/27843983
818:https://www.jstor.org/stable/27843983
810:can be seen on ancient Roman mosaics
7:
964:https://www.jstor.org/stable/3026946
485:This article is within the scope of
411:
409:
982:Improved to Good Article status by
428:It is of interest to the following
197:for discussing improvements to the
1469:High-priority mathematics articles
14:
1155:The American Mathematical Monthly
600:may be automatically archived by
505:Knowledge:WikiProject Mathematics
41:. If you can improve it further,
1005:be created to use some of them.
999:
915:
875:
822:https://arxiv.org/abs/1609.07779
784:
748:
553:
508:Template:WikiProject Mathematics
472:
462:
441:
410:
379:
219:Click here to start a new topic.
124:
19:
680:Please do not modify this page.
525:This article has been rated as
1430:11:53, 23 September 2023 (UTC)
1415:10:31, 23 September 2023 (UTC)
1393:10:15, 23 September 2023 (UTC)
1377:08:41, 23 September 2023 (UTC)
1309:
1305:
1291:
1273:
1261:
1246:
1168:10.1080/00029890.1969.12000217
29:has been listed as one of the
1:
1464:GA-Class mathematics articles
643:16:41, 1 September 2020 (UTC)
628:14:21, 1 September 2020 (UTC)
499:and see a list of open tasks.
216:Put new text under old text.
906:https://vimeo.com/286360639
693:Knowledge talk:Did you know
685:this nomination's talk page
669:12:42, 23 August 2024 (UTC)
224:New to Knowledge? Welcome!
158:The text of the entry was:
1485:
1057:10:41, 23 April 2022 (UTC)
1043:17:02, 19 April 2022 (UTC)
1029:05:02, 19 April 2022 (UTC)
1015:02:33, 19 April 2022 (UTC)
992:18:14, 18 April 2022 (UTC)
718:10:41, 23 April 2022 (UTC)
661:2A02:2168:B03:3F14:0:0:0:4
160:Did you know ... that the
1454:Mathematics good articles
1362:Relation to Umbilic torus
1145:Pappus's centroid theorem
524:
457:
436:
254:Be welcoming to newcomers
180:
65:
61:
33:Mathematics good articles
531:project's priority scale
137:appeared on Knowledge's
1449:Knowledge good articles
1356:03:26, 9 May 2022 (UTC)
1198:01:21, 4 May 2022 (UTC)
1132:17:43, 3 May 2022 (UTC)
1111:17:35, 3 May 2022 (UTC)
836:collar onto a garment?
689:the article's talk page
649:Did you know nomination
488:WikiProject Mathematics
1340:
793:holding a Möbius strip
603:Lowercase sigmabot III
418:This article is rated
249:avoid personal attacks
135:fact from this article
1341:
1138:Area of swept surface
990:). Self-nominated at
373:Auto-archiving period
274:Neutral point of view
39:good article criteria
1208:
511:mathematics articles
279:No original research
110:Good article nominee
91:Good article nominee
1243:
1228:
1336:
1329:
1321:
1229:
1211:
480:Mathematics portal
424:content assessment
260:dispute resolution
221:
66:Article milestones
1318:
1101:
995:
966:
948:
908:
868:
842:
824:
779:
671:
659:comment added by
610:
609:
545:
544:
541:
540:
537:
536:
404:
403:
240:Assume good faith
217:
188:
187:
119:
118:
57:
1476:
1345:
1343:
1342:
1337:
1319:
1317:
1316:
1301:
1269:
1268:
1256:
1245:
1242:
1237:
1227:
1219:
1184:
1119:Mobius M. Mobius
1079:
1076:Mobius M. Mobius
1070:Mobius M. Mobius
1003:
981:
961:
943:
919:
903:
879:
856:Source: Bagels:
855:
837:
815:
788:
774:
762:recycling symbol
754:recycling symbol
752:
704:The result was:
682:
605:
589:
557:
549:
513:
512:
509:
506:
503:
482:
477:
476:
466:
459:
458:
453:
445:
438:
421:
415:
414:
413:
406:
398:
384:
383:
374:
353:
352:
338:
269:Article policies
190:
181:Current status:
162:recycling symbol
128:
105:
86:
63:
46:
23:
16:
1484:
1483:
1479:
1478:
1477:
1475:
1474:
1473:
1439:
1438:
1403:my earlier edit
1364:
1308:
1260:
1206:
1205:
1151:
1140:
1072:
1067:
954:: ... that the
932:: ... that the
924:
923:
922:
892:: ... that the
884:
883:
882:
848:: ... that the
804:: ... that the
796:
795:
794:
757:
756:
755:
745:
743:
739:Article history
678:
651:
615:
613:Twice cut strip
601:
590:
584:
562:
510:
507:
504:
501:
500:
478:
471:
451:
422:on Knowledge's
419:
400:
399:
394:
371:
295:
290:
289:
288:
265:
235:
176:
175:
156:
101:
82:
12:
11:
5:
1482:
1480:
1472:
1471:
1466:
1461:
1456:
1451:
1441:
1440:
1437:
1436:
1435:
1434:
1433:
1432:
1422:David Eppstein
1385:David Eppstein
1363:
1360:
1359:
1358:
1335:
1332:
1327:
1324:
1315:
1311:
1307:
1304:
1300:
1296:
1293:
1290:
1287:
1284:
1281:
1278:
1275:
1272:
1267:
1263:
1259:
1255:
1251:
1248:
1241:
1236:
1232:
1226:
1223:
1218:
1214:
1190:David Eppstein
1186:
1185:
1139:
1136:
1135:
1134:
1124:David Eppstein
1071:
1068:
1066:
1065:
1064:
1063:
1062:
1061:
1060:
1059:
1021:David Eppstein
984:David Eppstein
979:
978:
977:
976:
967:
949:
920:
914:
913:
912:
911:
910:
909:
880:
874:
873:
872:
871:
870:
869:
843:
825:
789:
783:
782:
781:
780:
753:
747:
746:
742:
741:
736:
726:
724:
720:
702:
701:
673:
650:
647:
646:
645:
614:
611:
608:
607:
595:
592:
591:
586:
582:
580:
577:
576:
564:
563:
558:
552:
543:
542:
539:
538:
535:
534:
523:
517:
516:
514:
497:the discussion
484:
483:
467:
455:
454:
446:
434:
433:
427:
416:
402:
401:
392:
390:
389:
386:
385:
355:
354:
292:
291:
287:
286:
281:
276:
267:
266:
264:
263:
256:
251:
242:
236:
234:
233:
222:
213:
212:
209:
208:
202:
186:
185:
178:
177:
157:
132:
131:
129:
121:
120:
117:
116:
113:
106:
103:April 18, 2022
98:
97:
94:
87:
84:March 30, 2022
79:
78:
75:
72:
68:
67:
59:
58:
24:
13:
10:
9:
6:
4:
3:
2:
1481:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1446:
1444:
1431:
1427:
1423:
1418:
1417:
1416:
1412:
1408:
1407:Leon.Manukyan
1404:
1400:
1399:your reversal
1396:
1395:
1394:
1390:
1386:
1381:
1380:
1379:
1378:
1374:
1370:
1369:Leon.Manukyan
1361:
1357:
1353:
1349:
1333:
1330:
1325:
1322:
1313:
1302:
1298:
1294:
1288:
1285:
1282:
1279:
1276:
1270:
1265:
1257:
1253:
1249:
1239:
1234:
1230:
1224:
1221:
1216:
1212:
1202:
1201:
1200:
1199:
1195:
1191:
1183:
1180:
1176:
1173:
1169:
1165:
1161:
1157:
1156:
1150:
1149:
1148:
1146:
1137:
1133:
1129:
1125:
1120:
1115:
1114:
1113:
1112:
1108:
1104:
1099:
1095:
1091:
1087:
1083:
1077:
1069:
1058:
1054:
1050:
1046:
1045:
1044:
1040:
1036:
1032:
1031:
1030:
1026:
1022:
1018:
1017:
1016:
1012:
1008:
1002:
998:
997:
996:
993:
989:
985:
975:
971:
968:
965:
959:
958:
953:
950:
947:
941:
937:
936:
931:
928:
927:
926:
925:
918:
907:
901:
897:
896:
891:
888:
887:
886:
885:
878:
867:
863:
859:
853:
852:
847:
844:
841:
835:
834:
829:
826:
823:
819:
813:
809:
808:
803:
800:
799:
798:
797:
792:
787:
778:
772:
771:
766:
763:
760:... that the
759:
758:
751:
740:
737:
735:
731:
728:
727:
723:
721:
719:
715:
711:
707:
700:
698:
694:
690:
686:
681:
675:
674:
672:
670:
666:
662:
658:
648:
644:
640:
636:
632:
631:
630:
629:
625:
621:
612:
604:
599:
594:
593:
579:
578:
575:
574:
570:
566:
565:
561:
556:
551:
550:
547:
532:
528:
527:High-priority
522:
519:
518:
515:
498:
494:
490:
489:
481:
475:
470:
468:
465:
461:
460:
456:
452:High‑priority
450:
447:
444:
440:
435:
431:
425:
417:
408:
407:
388:
387:
382:
378:
370:
366:
363:
361:
357:
356:
351:
347:
344:
341:
337:
333:
329:
326:
323:
320:
317:
314:
311:
308:
305:
301:
298:
297:Find sources:
294:
293:
285:
284:Verifiability
282:
280:
277:
275:
272:
271:
270:
261:
257:
255:
252:
250:
246:
243:
241:
238:
237:
231:
227:
226:Learn to edit
223:
220:
215:
214:
211:
210:
206:
200:
196:
192:
191:
184:
179:
174:
172:
171:
164:
163:
154:
153:
148:
146:
145:Did you know?
140:
136:
130:
127:
123:
122:
114:
112:
111:
107:
104:
100:
99:
95:
93:
92:
88:
85:
81:
80:
76:
73:
70:
69:
64:
60:
55:
53:
52:
44:
40:
36:
35:
34:
28:
25:
22:
18:
17:
1365:
1187:
1159:
1153:
1141:
1073:
980:
969:
957:Möbius strip
955:
951:
939:
935:Möbius strip
933:
929:
899:
895:Möbius strip
893:
889:
851:Möbius strip
849:
845:
833:Möbius strip
831:
827:
811:
807:Möbius strip
805:
801:
770:Möbius strip
768:
764:
722:
705:
703:
696:
688:
684:
679:
676:
655:— Preceding
652:
616:
597:
567:
559:
546:
526:
486:
430:WikiProjects
376:
358:
345:
339:
331:
324:
318:
312:
306:
296:
268:
199:Möbius strip
193:This is the
183:Good article
182:
170:Möbius strip
168:
166:
159:
150:
142:
108:
89:
49:
47:
43:please do so
31:
30:
27:Möbius strip
26:
1162:: 355–366,
502:Mathematics
493:mathematics
449:Mathematics
322:free images
205:not a forum
152:May 3, 2022
1443:Categories
1080:(Sources:
940:(pictured)
900:(pictured)
812:(pictured)
767:depicts a
765:(pictured)
620:Cmdrscotty
167:depicts a
165:(pictured)
149:column on
96:Not listed
37:under the
864:– Pasta:
860:– Bacon:
262:if needed
245:Be polite
195:talk page
139:Main Page
970:Reviewed
962:Source:
944:Source:
904:Source:
838:Source:
816:Source:
775:Source:
706:promoted
657:unsigned
598:365 days
560:Archives
420:GA-class
377:365 days
360:Archives
230:get help
203:This is
201:article.
51:reassess
1182:0240702
1175:2316426
1074:Should
1049:Kingsif
1035:Thriley
1007:Thriley
730:Comment
710:Kingsif
635:Ag2gaeh
529:on the
328:WP refs
316:scholar
141:in the
74:Process
1348:Ovinus
1103:Sahaib
426:scale.
300:Google
115:Listed
77:Result
1172:JSTOR
343:JSTOR
304:books
258:Seek
1426:talk
1411:talk
1389:talk
1373:talk
1352:talk
1194:talk
1128:talk
1107:talk
1053:talk
1039:talk
1025:talk
1011:talk
988:talk
952:ALT6
930:ALT5
890:ALT4
846:ALT3
828:ALT2
820:and
802:ALT1
791:Aion
734:view
714:talk
665:talk
639:talk
624:talk
521:High
336:FENS
310:news
247:and
71:Date
1401:of
1286:cos
1164:doi
732:or
708:by
691:or
350:TWL
1445::
1428:)
1413:)
1391:)
1375:)
1354:)
1346:.
1289:
1231:∫
1225:π
1213:∫
1196:)
1179:MR
1177:,
1170:,
1160:76
1158:,
1130:)
1109:)
1096:,
1092:,
1088:,
1084:,
1055:)
1041:)
1027:)
1013:)
972::
942:?
902:?
814:?
773:?
725:(
716:)
687:,
667:)
641:)
626:)
571:,
375::
367:,
330:)
228:;
133:A
54:it
45:.
1424:(
1420:—
1409:(
1387:(
1371:(
1350:(
1334:s
1331:d
1326:t
1323:d
1314:2
1310:)
1306:)
1303:2
1299:/
1295:s
1292:(
1283:t
1280:+
1277:1
1274:(
1271:+
1266:2
1262:)
1258:2
1254:/
1250:t
1247:(
1240:1
1235:0
1222:2
1217:0
1192:(
1188:—
1166::
1126:(
1105:(
1100:)
1098:5
1094:4
1090:3
1086:2
1082:1
1051:(
1037:(
1023:(
1009:(
994:.
986:(
744:)
712:(
699:.
663:(
637:(
622:(
573:2
569:1
533:.
432::
369:2
365:1
362::
346:·
340:·
332:·
325:·
319:·
313:·
307:·
302:(
232:.
173:?
155:.
147:"
143:"
56:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
