785:
for numbers 1 to 9 (I, II, III, IV, V, VI, VII, VIII, IX). Unlike the Roman notation, there are only symbols for numbers one ("I") and five ("U"), protruding off the side of a vertical stroke, or stem, which has no numeric value by itself. In some inscriptions the notches are placed horizontally on a
797:, resembling the letter "P" in combination with the stem. 10 is represented by two turned U's opposing each other. More numbers up to 19 or 20, can be represented by a combination of I's and U's branching off of a stem, similar to how Roman numerals are represented by combinations of I's and V's.
911:
31:
968:
respectively. It is unclear if the notation can represent all numbers unambiguously; for example, it may not be possible to distinguish 1010 from 100.
38:
show the use of "pentadic" runic numerals to replace the Arabic numerals in representing dates. The number shown here as zero is normally used for ten.
768:
910:
of an 18 year-old journeyman tailor, Edward
Larsson, that are dated to 1885 in pentadic runes. A copy of the note was first published by the
488:
321:
930:
793:
The number 4 is represented by four vertical lines on the horizontal stem, 5 is represented by what looks like a half-turned letter
1092:
112:
907:
555:
35:
1225:
761:
336:
681:
691:
508:
862:. On older runic calendars, a different notation for representing the Golden Numbers was used; the 16 runes of
568:
30:
936:
The authors of the North
American rune stones do not seem to understand the positional notation or the concept of
664:
433:
754:
81:
1011:
The number 10 is represented in Roman numerals as "X" which is two turned V's opposing each other: "><".
744:
528:
125:
926:
428:
344:
790:
of the rune; on other inscriptions the stave is horizontal and the "I" and inverted "U" rise off of it.
546:
917:
This positional notation however appears on two unrelated sets of rune stones allegedly discovered in
922:
641:
502:
495:
376:
896:
723:
588:
539:
351:
283:
138:
99:
1199:
1191:
848:
830:
636:
389:
226:
221:
168:
1220:
1183:
1107:
880:(1588ā1654), uses this futhark notation, and not the pentadic numerals under discussion here.
718:
708:
696:
676:
631:
626:
562:
394:
273:
206:
196:
183:
148:
143:
1031:
1175:
872:
839:
822:
621:
515:
268:
256:
201:
191:
158:
133:
46:
900:
863:
814:
733:
703:
646:
616:
601:
361:
329:
301:
278:
261:
120:
713:
992:
889:
851:
810:
806:
782:
728:
671:
651:
606:
479:
211:
178:
163:
89:
62:
1214:
1203:
1115:
1051:
987:
918:
534:
423:
356:
296:
231:
173:
153:
20:
686:
611:
1139:
1073:
941:
855:
656:
521:
473:
463:
58:
54:
937:
859:
844:
458:
216:
1187:
1111:
977:
468:
876:
manuscript, originally from 1328, but collected and published by the Dane
1069:
893:
877:
870:, runes were improvised for the numbers 17, 18, and 19. For example, the
1195:
1103:
453:
438:
24:
443:
1179:
1157:
912:
Institute for
Dialectology, Onomastics and Folklore Research in UmeƄ
982:
945:
448:
410:
371:
29:
66:
1106:, Sv: Dialekt-, ortnamns-, och folkminnesarkivet i UmeĆ„: 5ā6.
903:. It is unknown if this use existed before the 19th century.
888:
In some peculiar instances runic numbers have been used as
1166:
Hagen, S. N. (1950). "The
Kensington Runic Inscription".
794:
1142:(transcription). number 3], lines 3 and 8.
805:
The widest use of the notation is in presenting the
53:) are a notation for presenting numbers, usually by
940:. The rune for 10 is used interchangeably for 0,
906:The oldest authenticated use of this notation is
57:in wood or stone. The notation has been used in
866:represented the numbers from 1 to 16 and three
762:
8:
854:. It is unknown if they were in use in the
929:found in 1971. All refer to pre-Columbian
769:
755:
105:
76:
1159:The Kensington Rune Stone: A Study Guide
952:from Spirit Pond contains the sequences
925:found in 1898; the second are the three
1023:
1004:
88:
843:). The numbers are commonly found in
781:The notation is similar to the older
23:. For the pental numeral system, see
16:Runic notation for presenting numbers
7:
14:
1074:"The Runic Calendar from Gotland"
931:Norse exploration of the Americas
1091:Skƶld, Tryggve (Winter 2003).
1032:"1 to 100 Roman Numbers Chart"
61:, usually in conjunction with
1:
948:with little consistency. The
1242:
1156:Bengtson, John D. (n.d.),
960:, which have been read as
489:Non-standard radices/bases
18:
1093:"Edward Larssons alfabet"
801:Dating and extent of use
19:For 5-adic numbers, see
745:List of numeral systems
927:Spirit Pond runestones
834:
826:
818:
50:
39:
113:HinduāArabic numerals
33:
1226:Modern runic writing
923:Kensington Runestone
642:Prehistoric counting
418:Common radices/bases
100:Place-value notation
65:and inscriptions in
1080:. Computus Runicus.
921:. The first is the
884:Positional notation
858:, let alone in the
589:Sign-value notation
245:East Asian systems
51:pentadiska siffror
40:
950:inscription stone
897:positional system
786:vertical stem or
779:
778:
578:
577:
43:Pentadic numerals
34:Edward Larsson's
1233:
1207:
1162:
1144:
1143:
1136:
1130:
1129:
1127:
1126:
1120:
1114:. Archived from
1097:
1088:
1082:
1081:
1066:
1060:
1059:
1052:"Rune calendars"
1048:
1042:
1041:
1039:
1038:
1028:
1012:
1009:
899:, replacing the
873:Computus Runicus
849:Early Modern Age
837:, also known as
771:
764:
757:
560:
544:
526:
516:balanced ternary
513:
500:
106:
77:
1241:
1240:
1236:
1235:
1234:
1232:
1231:
1230:
1211:
1210:
1180:10.2307/2854163
1165:
1155:
1152:
1150:Further reading
1147:
1138:
1137:
1133:
1124:
1122:
1118:
1095:
1090:
1089:
1085:
1078:arild-hauge.com
1068:
1067:
1063:
1050:
1049:
1045:
1036:
1034:
1030:
1029:
1025:
1021:
1016:
1015:
1010:
1006:
1001:
974:
901:Arabic numerals
886:
864:Younger Futhark
852:calendar sticks
811:Runic calendars
803:
775:
739:
738:
661:
647:Proto-cuneiform
592:
591:
580:
579:
574:
573:
558:
542:
524:
511:
498:
485:
414:
413:
401:
400:
381:
341:
326:
317:
316:
307:
306:
288:
247:
246:
237:
236:
188:
130:
116:
115:
103:
102:
90:Numeral systems
75:
63:runic calendars
36:notes from 1885
28:
17:
12:
11:
5:
1239:
1237:
1229:
1228:
1223:
1213:
1212:
1209:
1208:
1174:(3): 321ā356.
1163:
1151:
1148:
1146:
1145:
1131:
1102:(in Swedish).
1083:
1061:
1043:
1022:
1020:
1017:
1014:
1013:
1003:
1002:
1000:
997:
996:
995:
993:Runic calendar
990:
985:
980:
973:
970:
885:
882:
835:kalenderstavar
807:Golden Numbers
802:
799:
783:Roman numerals
777:
776:
774:
773:
766:
759:
751:
748:
747:
741:
740:
737:
736:
731:
726:
721:
716:
711:
706:
701:
700:
699:
694:
689:
679:
674:
668:
667:
660:
659:
654:
649:
644:
639:
634:
629:
624:
619:
614:
609:
604:
598:
597:
596:Non-alphabetic
593:
587:
586:
585:
582:
581:
576:
575:
572:
571:
566:
553:
537:
532:
519:
506:
492:
491:
484:
483:
476:
471:
466:
461:
456:
451:
446:
441:
436:
431:
426:
420:
419:
415:
408:
407:
406:
403:
402:
399:
398:
392:
386:
385:
380:
379:
374:
369:
364:
359:
354:
348:
347:
345:Post-classical
340:
339:
333:
332:
325:
324:
318:
314:
313:
312:
309:
308:
305:
304:
299:
293:
292:
287:
286:
281:
276:
271:
266:
265:
264:
253:
252:
248:
244:
243:
242:
239:
238:
235:
234:
229:
224:
219:
214:
209:
204:
199:
194:
187:
186:
181:
176:
171:
166:
161:
156:
151:
146:
141:
136:
129:
128:
126:Eastern Arabic
123:
121:Western Arabic
117:
111:
110:
109:
104:
98:
97:
96:
93:
92:
86:
85:
74:
71:
15:
13:
10:
9:
6:
4:
3:
2:
1238:
1227:
1224:
1222:
1219:
1218:
1216:
1205:
1201:
1197:
1193:
1189:
1185:
1181:
1177:
1173:
1169:
1164:
1161:
1160:
1154:
1153:
1149:
1141:
1140:"Spirit Pond"
1135:
1132:
1121:on 2010-08-17
1117:
1113:
1109:
1105:
1101:
1094:
1087:
1084:
1079:
1075:
1071:
1065:
1062:
1057:
1053:
1047:
1044:
1033:
1027:
1024:
1018:
1008:
1005:
998:
994:
991:
989:
988:Pental system
986:
984:
981:
979:
976:
975:
971:
969:
967:
963:
959:
955:
951:
947:
943:
939:
934:
932:
928:
924:
920:
919:North America
915:
913:
909:
904:
902:
898:
895:
891:
883:
881:
879:
875:
874:
869:
865:
861:
857:
853:
850:
847:and possibly
846:
842:
841:
836:
832:
828:
824:
820:
819:kalenderstave
816:
812:
808:
800:
798:
796:
791:
789:
784:
772:
767:
765:
760:
758:
753:
752:
750:
749:
746:
743:
742:
735:
732:
730:
727:
725:
722:
720:
717:
715:
712:
710:
707:
705:
702:
698:
695:
693:
690:
688:
685:
684:
683:
682:Alphasyllabic
680:
678:
675:
673:
670:
669:
666:
663:
662:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
599:
595:
594:
590:
584:
583:
570:
567:
564:
557:
554:
551:
550:
541:
538:
536:
533:
530:
523:
520:
517:
510:
507:
504:
497:
494:
493:
490:
487:
486:
481:
477:
475:
472:
470:
467:
465:
462:
460:
457:
455:
452:
450:
447:
445:
442:
440:
437:
435:
432:
430:
427:
425:
422:
421:
417:
416:
412:
405:
404:
396:
393:
391:
388:
387:
383:
382:
378:
375:
373:
370:
368:
365:
363:
360:
358:
355:
353:
350:
349:
346:
343:
342:
338:
335:
334:
331:
328:
327:
323:
320:
319:
315:Other systems
311:
310:
303:
300:
298:
297:Counting rods
295:
294:
290:
289:
285:
282:
280:
277:
275:
272:
270:
267:
263:
260:
259:
258:
255:
254:
250:
249:
241:
240:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
200:
198:
195:
193:
190:
189:
185:
182:
180:
177:
175:
172:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
140:
137:
135:
132:
131:
127:
124:
122:
119:
118:
114:
108:
107:
101:
95:
94:
91:
87:
83:
79:
78:
72:
70:
68:
64:
60:
56:
52:
48:
44:
37:
32:
26:
22:
21:p-adic number
1171:
1167:
1158:
1134:
1123:. Retrieved
1116:the original
1099:
1086:
1077:
1064:
1055:
1046:
1035:. Retrieved
1026:
1007:
965:
961:
957:
953:
949:
935:
916:
908:in the notes
905:
887:
871:
867:
838:
804:
792:
787:
780:
548:
509:Signed-digit
384:Contemporary
366:
251:Contemporary
42:
41:
1056:Gangleri.nl
946:<1,0>
856:Middle Ages
687:Akį¹£arapallÄ«
657:Tally marks
556:Non-integer
59:Scandinavia
1215:Categories
1125:2009-06-02
1100:DAUM-katta
1037:2023-08-23
1019:References
860:Viking Age
845:Modern Age
809:, 1ā19 on
724:Glagolitic
697:Kaį¹apayÄdi
665:Alphabetic
569:Asymmetric
411:radix/base
352:Cistercian
337:Babylonian
284:Vietnamese
139:Devanagari
55:inscribing
1204:162374269
1188:0038-7134
1112:1401-548X
999:Footnotes
978:Biquinary
966:year 1010
962:year 1011
914:in 2004.
831:Norwegian
827:runstavar
692:Äryabhaį¹a
637:Kharosthi
529:factorial
496:Bijective
397:(IƱupiaq)
227:Sundanese
222:Mongolian
169:Malayalam
1221:Numerals
1168:Speculum
1072:(1328).
1070:Ole Worm
972:See also
894:base ten
890:numerals
878:Ole Worm
719:Georgian
709:Cyrillic
677:Armenian
632:Etruscan
627:Egyptian
535:Negative
395:Kaktovik
390:Cherokee
367:Pentadic
291:Historic
274:Japanese
207:Javanese
197:Balinese
184:Dzongkha
149:Gurmukhi
144:Gujarati
82:a series
80:Part of
73:Notation
1196:2854163
954:ahr:011
823:Swedish
622:Chuvash
540:Complex
330:Ancient
322:History
269:Hokkien
257:Chinese
202:Burmese
192:Tibetan
179:Kannada
159:Sinhala
134:Bengali
47:Swedish
25:Quinary
1202:
1194:
1186:
1110:
958:ahr:00
944:, and
868:ad hoc
815:Danish
734:Hebrew
704:Coptic
617:Brahmi
602:Aegean
559:
543:
525:
512:
499:
362:Muisca
302:Tangut
279:Korean
262:Suzhou
174:Telugu
1200:S2CID
1192:JSTOR
1119:(PDF)
1096:(PDF)
983:Ogham
892:in a
840:clogs
729:Greek
714:GeŹ½ez
672:Abjad
652:Roman
612:Aztec
607:Attic
522:Mixed
480:table
372:Quipu
357:Mayan
212:Khmer
164:Tamil
67:runes
1184:ISSN
1108:ISSN
1104:UmeƄ
964:and
956:and
938:zero
788:stav
377:Rumi
232:Thai
154:Odia
1176:doi
409:By
217:Lao
1217::
1198:.
1190:.
1182:.
1172:25
1170:.
1098:.
1076:.
1054:.
942:10
933:.
833::
829:,
825::
821:,
817::
474:60
469:20
464:16
459:12
454:10
84:on
69:.
49::
1206:.
1178::
1128:.
1058:.
1040:.
813:(
795:U
770:e
763:t
756:v
565:)
563:Ļ
561:(
552:)
549:i
547:2
545:(
531:)
527:(
518:)
514:(
505:)
503:1
501:(
482:)
478:(
449:8
444:6
439:5
434:4
429:3
424:2
45:(
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
