25:
114:
90:
98:
172:
903:, and perhaps a representation of 4 lines or 4 directions. However, the other unit numerals appear to be arbitrary symbols in even the oldest inscriptions. It is sometimes supposed that they may also have come from collections of strokes, run together in cursive writing in a way similar to that attested in the development of Egyptian
915:
The sometimes rather striking graphic similarity they have with the hieratic and demotic
Egyptian numerals, while suggestive, is not prima facie evidence of an historical connection, as many cultures have independently recorded numbers as collections of strokes. With a similar writing instrument, the
940:
and šØ£. However, there are problems of timing and lack of records. The full set of numerals is not attested until the 1st-2nd century CE, 400 years after Ashoka. Assertions that either the numerals derive from tallies or that they are alphabetic are, at best, educated guesses.
935:
alphabet. For instance, 4 "chatur" early on took a shape much like the
Kharosthi letter šØ "ch", while 5 "pancha" looks remarkably like Kharosthi šØ¤ "p"; and so on through 6 "ssat" and šØ®, then 7 "sapta" and šØÆ, and finally 9
916:
cursive forms of such groups of strokes could easily be broadly similar as well, and this is one of the primary hypotheses for the origin of Brahmi numerals,There is a possibility that it came from
Chinese Shang numerals
911:
numerals, but this is not supported by any direct evidence. Likewise, the units for the tens are not obviously related to each other or to the units, although 10, 20, 80, 90 might be based on a circle.
1885:
1850:
159:. Later additions to the system included separate symbols for each multiple of 10 (e.g. 20, 30, and 40). There were also symbols for 100 and 1000, which were combined in
2037:
1587:
1862:
54:
1283:
2017:
1909:
163:
with the units to signify 200, 300, 2000, 3000, etc. In computers, these ligatures are written with the Brahmi Number Joiner at U+1107F.
1804:
1979:
1241:
870:
2032:
590:
2042:
1984:
1557:
423:
2027:
1537:
1238:
76:
47:
1276:
1777:
214:
148:
2012:
1627:
1381:
1208:
657:
1421:
1300:
863:
438:
125:
2002:
1227:
783:
2022:
2007:
1269:
610:
151:. However, the Brahmi numeral system was conceptually distinct from these later systems, as it was a non-
793:
1517:
670:
1527:
766:
535:
37:
883:
The source of the first three numerals seems clear: they are collections of 1, 2, and 3 strokes, in
2068:
1817:
1683:
1532:
856:
183:
41:
33:
1943:
1825:
1416:
1249:
846:
630:
227:
491:
1964:
1891:
530:
446:
58:
1704:
1821:
1813:
1315:
648:
1903:
1614:
1582:
743:
604:
597:
478:
160:
930:
8:
1969:
1938:
1746:
1732:
1669:
1562:
1507:
1502:
1456:
1406:
825:
815:
690:
641:
453:
385:
240:
201:
152:
144:
280:
1471:
1292:
1245:
908:
738:
328:
323:
270:
275:
2063:
1974:
1856:
1676:
1451:
1446:
1320:
1234:
1202:
820:
810:
798:
778:
733:
728:
664:
496:
468:
375:
308:
298:
285:
250:
245:
895:. In the oldest inscriptions, 4 looks like a +, reminiscent of the X of neighboring
713:
1690:
1572:
1542:
1512:
1222:
The
Universal History of Numbers: From Prehistory to the Invention of the Computer.
892:
723:
617:
370:
358:
303:
293:
260:
235:
113:
102:
1655:
1426:
1897:
1844:
1718:
1567:
1436:
1257:
835:
805:
748:
703:
463:
431:
403:
380:
363:
222:
1476:
1396:
1190:
318:
1868:
1788:
1725:
1648:
1634:
1552:
1547:
1481:
1325:
924:
830:
773:
753:
708:
581:
313:
265:
191:
140:
118:
89:
1376:
896:
2057:
1948:
1880:
1809:
1711:
1169:
888:
636:
525:
458:
398:
333:
255:
97:
1371:
1335:
1915:
1753:
1697:
1641:
1461:
1441:
1366:
788:
147:
from the 3rd century BCE. It is the direct graphic ancestor of the modern
928:
897:
1921:
1874:
1662:
1608:
1391:
1345:
758:
623:
575:
565:
1620:
1577:
1431:
1411:
1386:
560:
171:
156:
1739:
1401:
1361:
1261:
920:
570:
1522:
1486:
1466:
904:
129:
121:
1340:
555:
540:
106:
1588:
Shanti Swarup
Bhatnagar Prize recipients in Mathematical Science
132:, therefore 232 CE, clearly appears behind the head of the king.
1330:
1232:
Number Words and Number
Symbols - A Cultural History of Numbers
884:
545:
1224:
Translated by David Bellos, Sophie Wood, pub. J. Wiley, 2000.
550:
512:
473:
1789:
Infinite series expansions for the trigonometric functions
2038:
Ramanujan
Institute for Advanced Study in Mathematics
1783:
93:
Evolution of Brahmi numerals from the time of Ashoka.
16:
Numeral system predating modern Hindu-Arabic numerals
124:(232 CE). The minting date, here 153 (100-50-3 in
2055:
46:but its sources remain unclear because it lacks
919:Another possibility is that the numerals were
1277:
864:
175:Brahmi numerals signs of the 2nd century CE.
1805:Kerala school of astronomy and mathematics
1284:
1270:
871:
857:
77:Learn how and when to remove this message
2033:Homi Bhabha Centre for Science Education
891:, but soon becoming horizontal like the
170:
112:
96:
88:
2056:
1291:
1265:
1188:
155:decimal system, and did not include
18:
1558:Subbayya Sivasankaranarayana Pillai
1191:"File:Shang numerals to brahmi.jpg"
13:
2018:Institute of Mathematical Sciences
14:
2080:
2028:Harish-Chandra Research Institute
1538:K. R. Parthasarathy (probabilist)
887:'s era vertical I, II, III like
23:
2013:Chennai Mathematical Institute
1382:Melpathur Narayana Bhattathiri
1182:
1:
1175:
101:The number "256" in Ashoka's
2003:Indian Statistical Institute
1228:Karl Menninger (mathematics)
7:
2023:Indian Institute of Science
2008:Bhaskaracharya Pratishthana
1886:A. A. Krishnaswamy Ayyangar
1851:Shankar Balakrishna Dikshit
1778:HinduāArabic numeral system
1163:
944:
929:
898:
149:HinduāArabic numeral system
10:
2085:
1518:Subrahmanyan Chandrasekhar
1207:: CS1 maint: url-status (
591:Non-standard radices/bases
166:
1993:
1957:
1931:
1835:
1797:
1763:
1600:
1528:Veeravalli S. Varadarajan
1495:
1354:
1308:
1299:
1254:The HinduāArabic Numerals
1087:Zero place-holder system
1944:Henry Thomas Colebrooke
1533:S. R. Srinivasa Varadhan
950:Ancient non-Zero system
32:This article includes a
1417:MÄdhava of Saį¹
gamagrÄma
1250:Louis Charles Karpinski
847:List of numeral systems
61:more precise citations.
1092:HinduāArabic numerals
955:HinduāArabic numerals
176:
133:
126:Brahmi script numerals
110:
94:
1628:BrÄhmasphuį¹asiddhÄnta
215:HinduāArabic numerals
174:
116:
100:
92:
1904:T. A. Saraswati Amma
1615:Bakhshali manuscript
1583:Kannan Soundararajan
893:Han Chinese numerals
744:Prehistoric counting
520:Common radices/bases
202:Place-value notation
1980:Islamic mathematics
1939:Walter Eugene Clark
1733:Vasishtha Siddhanta
1705:SiddhÄnta Shiromani
1684:Paitamaha Siddhanta
1563:Tilak Raj Prabhakar
1508:Satyendra Nath Bose
1503:Srinivasa Ramanujan
1457:Nilakantha Somayaji
1189:Naus, Naus (2020).
1088:
951:
927:, and based on the
691:Sign-value notation
145:Indian subcontinent
1472:Gangesha Upadhyaya
1293:Indian mathematics
1246:David Eugene Smith
1086:
949:
347:East Asian systems
177:
134:
111:
95:
34:list of references
2051:
2050:
1857:Sudhakara Dvivedi
1677:Paulisa Siddhanta
1596:
1595:
1452:Jagannatha Samrat
1447:Achyuta Pisharati
1161:
1160:
1084:
1083:
881:
880:
680:
679:
87:
86:
79:
2076:
1691:Romaka Siddhanta
1573:Akshay Venkatesh
1543:M. S. Narasimhan
1513:P.C. Mahalanobis
1306:
1305:
1286:
1279:
1272:
1263:
1262:
1213:
1212:
1206:
1198:
1186:
1127:Brahmi numerals
1089:
1085:
1020:Brahmi numerals
952:
948:
934:
901:
873:
866:
859:
662:
646:
628:
618:balanced ternary
615:
602:
208:
207:
179:
178:
143:attested in the
109:(circa 250 BCE).
103:Minor Rock Edict
82:
75:
71:
68:
62:
57:this article by
48:inline citations
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2069:Brahmic scripts
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1989:
1953:
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1898:C. T. Rajagopal
1845:Bapudeva Sastri
1837:
1831:
1793:
1773:Brahmi numerals
1765:
1759:
1719:Surya Siddhanta
1592:
1568:Manjul Bhargava
1491:
1350:
1295:
1290:
1220:Georges Ifrah,
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1216:
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749:Proto-cuneiform
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192:Numeral systems
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137:Brahmi numerals
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38:related reading
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1482:Sankara Variar
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1301:Mathematicians
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925:Attic numerals
889:Roman numerals
879:
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849:
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839:
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141:numeral system
119:Western Satrap
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848:
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844:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
800:
797:
795:
792:
790:
787:
786:
785:
784:Alphasyllabic
782:
780:
777:
775:
772:
771:
768:
765:
764:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
735:
732:
730:
727:
725:
722:
720:
717:
715:
712:
710:
707:
705:
702:
701:
697:
696:
692:
686:
685:
672:
669:
666:
659:
656:
653:
652:
643:
640:
638:
635:
632:
625:
622:
619:
612:
609:
606:
599:
596:
595:
592:
589:
588:
583:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
523:
519:
518:
514:
507:
506:
498:
495:
493:
490:
489:
485:
484:
480:
477:
475:
472:
470:
467:
465:
462:
460:
457:
455:
452:
451:
448:
445:
444:
440:
437:
436:
433:
430:
429:
425:
422:
421:
417:Other systems
413:
412:
405:
402:
400:
399:Counting rods
397:
396:
392:
391:
387:
384:
382:
379:
377:
374:
372:
369:
365:
362:
361:
360:
357:
356:
352:
351:
343:
342:
335:
332:
330:
327:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
291:
287:
284:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
233:
229:
226:
224:
221:
220:
216:
210:
209:
203:
197:
196:
193:
190:
189:
185:
181:
180:
173:
164:
162:
158:
154:
150:
146:
142:
138:
131:
127:
123:
120:
115:
108:
104:
99:
91:
81:
78:
70:
60:
56:
50:
49:
43:
39:
35:
30:
21:
20:
1996:institutions
1916:K. S. Shukla
1888:(1892ā 1953)
1772:
1754:Yavanajataka
1752:
1745:
1738:
1731:
1724:
1717:
1712:Åulba SÅ«tras
1710:
1703:
1698:Sadratnamala
1696:
1689:
1682:
1675:
1668:
1661:
1654:
1647:
1642:Kanakkusaram
1640:
1633:
1626:
1619:
1607:
1477:VarÄhamihira
1442:Parameshvara
1397:GovindasvÄmi
1367:Äryabhaį¹a II
1253:
1231:
1221:
1194:
1184:
937:
918:
914:
882:
718:
650:
611:Signed-digit
486:Contemporary
353:Contemporary
136:
135:
73:
64:
53:Please help
45:
1932:Translators
1924:(1919ā2005)
1922:K. V. Sarma
1918:(1918ā2007)
1912:(1918ā1992)
1906:(1918ā2000)
1900:(1903ā1978)
1894:(1901ā1954)
1892:A. N. Singh
1877:(1888ā1958)
1875:B. B. Datta
1871:(1876ā1962)
1865:(1861ā1916)
1859:(1855ā1910)
1853:(1853ā1898)
1847:(1821ā1900)
1838:mathematics
1782:Symbol for
1766:innovations
1663:Lokavibhaga
1609:Aryabhatiya
1407:Jyeį¹£į¹hadeva
1392:Brahmagupta
1377:BhÄskara II
1362:Äryabhaį¹a I
1346:Yajnavalkya
923:, like the
789:Akį¹£arapallÄ«
759:Tally marks
658:Non-integer
59:introducing
2058:Categories
1881:T. Hayashi
1764:Pioneering
1747:YuktibhÄį¹£Ä
1670:PÄtÄ«gaį¹ita
1621:Bijaganita
1578:Ravi Vakil
1432:Munishvara
1412:Kamalakara
1387:Brahmadeva
1372:BhÄskara I
1321:Baudhayana
1176:References
921:acrophonic
826:Glagolitic
799:Kaį¹apayÄdi
767:Alphabetic
671:Asymmetric
513:radix/base
454:Cistercian
439:Babylonian
386:Vietnamese
241:Devanagari
153:positional
1910:S. N. Sen
1818:New Delhi
1740:Veį¹vÄroha
1601:Treatises
1402:Halayudha
1355:Classical
1326:Katyayana
1316:Apastamba
931:Kharoį¹£į¹hÄ«
899:Kharoį¹£į¹hÄ«
794:Äryabhaį¹a
739:Kharosthi
631:factorial
598:Bijective
499:(IƱupiaq)
329:Sundanese
324:Mongolian
271:Malayalam
161:ligatures
128:) of the
67:July 2012
2064:Numerals
1826:Varanasi
1784:zero (0)
1656:LÄ«lÄvatÄ«
1523:C.R. Rao
1487:Virasena
1467:Sridhara
1437:Narayana
1422:MahÄvÄ«ra
1203:cite web
1164:See also
945:Numerals
905:hieratic
821:Georgian
811:Cyrillic
779:Armenian
734:Etruscan
729:Egyptian
637:Negative
497:Kaktovik
492:Cherokee
469:Pentadic
393:Historic
376:Japanese
309:Javanese
299:Balinese
286:Dzongkha
251:Gurmukhi
246:Gujarati
184:a series
182:Part of
130:Saka era
122:Damasena
117:Coin of
105:No.1 in
1965:Babylon
1798:Centres
1462:ÅrÄ«pati
1341:Pingala
1309:Ancient
1256:(1911)
909:demotic
724:Chuvash
642:Complex
432:Ancient
424:History
371:Hokkien
359:Chinese
304:Burmese
294:Tibetan
281:Kannada
261:Sinhala
236:Bengali
167:Origins
107:Sasaram
55:improve
1994:Modern
1985:Europe
1975:Greece
1822:Ujjain
1814:Jaipur
1496:Modern
1336:PÄį¹ini
1331:Manava
1237:
885:Ashoka
836:Hebrew
806:Coptic
719:Brahmi
704:Aegean
661:
645:
627:
614:
601:
464:Muisca
404:Tangut
381:Korean
364:Suzhou
276:Telugu
139:are a
1970:China
1015:1000
831:Greek
816:GeŹ½ez
774:Abjad
754:Roman
714:Aztec
709:Attic
624:Mixed
582:table
474:Quipu
459:Mayan
314:Khmer
266:Tamil
40:, or
2043:TIFR
1248:and
1235:ISBN
1209:link
1195:Wiki
938:nava
907:and
479:Rumi
334:Thai
256:Odia
157:zero
1157:šÆ
1080:š„
1012:100
511:By
319:Lao
2060::
1824:,
1820:,
1816:,
1252:,
1230:,
1205:}}
1201:{{
1193:.
1154:š®
1151:š
1148:š¬
1145:š«
1142:šŖ
1139:š©
1136:šØ
1133:š§
1130:š¦
1122:9
1077:š¤
1074:š£
1071:š¢
1068:š”
1065:š
1062:š
1059:š
1056:š
1053:š
1050:š
1047:š
1044:š
1041:š
1038:š
1035:š
1032:š
1029:š
1026:š
1023:š
1009:90
1006:80
1003:70
1000:60
997:50
994:40
991:30
988:20
985:10
576:60
571:20
566:16
561:12
556:10
186:on
44:,
36:,
1828:)
1812:(
1285:e
1278:t
1271:v
1211:)
1197:.
1119:8
1116:7
1113:6
1110:5
1107:4
1104:3
1101:2
1098:1
1095:0
982:9
979:8
976:7
973:6
970:5
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964:3
961:2
958:1
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858:v
667:)
665:Ļ
663:(
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651:i
649:2
647:(
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629:(
620:)
616:(
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605:1
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580:(
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531:3
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80:)
74:(
69:)
65:(
51:.
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