1198:
72:
1170:
670:
505:
1264:
970:
540:
824:
737:
920:
2067:
2032:
856:
780:
696:
1000:
568:
104:
598:
2219:
1769:
2044:
1465:
603:
438:
2199:
2091:
1986:
2161:
2214:
2224:
2166:
1407:
1266:. The images in this section are color-coded so that the digital root of 1 is dark and the digital root of (base-1) is light.
1212:
1739:
2209:
1719:
1389:
1371:
1458:
1959:
940:
510:
2194:
1809:
1563:
1209:(or number base) can be calculated to analyse the symmetric patterns that arise. Using the calculation above,
53:
when the product of the row and column headings is divided by 9 (with remainder 0 represented by 9). Numerous
1603:
1482:
2184:
739:, where the element 9 is representative of the residue class of 0 rather than the traditional choice of 0.
17:
785:
2250:
2245:
2204:
2189:
1451:
701:
1699:
1417:
1709:
1173:
Slices of a Vedic cube (upper figures), and trimetric projections of the cells of given digital root
927:
869:
75:
Highlighting specific numbers within the Vedic square reveals distinct shapes each with some form of
1999:
1865:
1714:
2125:
2007:
1598:
829:
753:
2146:
2073:
1886:
675:
2003:
1995:
1497:
985:
553:
89:
2085:
1796:
1764:
1186:
42:
8:
2151:
2120:
1928:
1914:
1851:
1744:
1689:
1684:
1638:
1588:
1427:
1339:
743:
577:
76:
1653:
1474:
1382:
The
Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching
1280:
935:
931:
546:
31:
2156:
2038:
1858:
1633:
1628:
1502:
1433:
1403:
1385:
1367:
1872:
1754:
1724:
1694:
1318:
1306:
1197:
1837:
1608:
2079:
2026:
1954:
1900:
1749:
1618:
747:
1658:
1578:
2050:
1970:
1907:
1830:
1816:
1734:
1729:
1663:
1507:
1558:
571:
refers to the abstract "multiplication" between the elements of this monoid).
2239:
2130:
2062:
1991:
1893:
1437:
543:
71:
64:
can be observed in a Vedic square, some of which can be found in traditional
1553:
1517:
2097:
1935:
1879:
1823:
1643:
1623:
1548:
1275:
1182:
973:
923:
46:
1323:
2103:
2056:
1844:
1790:
1573:
1527:
972:. Every column and row includes all six numbers - so this subset forms a
65:
1802:
1759:
1613:
1593:
1568:
61:
1921:
1583:
1543:
1443:
665:{\displaystyle ((\mathbb {Z} /9\mathbb {Z} )^{\times },\{1,\circ \})}
500:{\displaystyle ((\mathbb {Z} /9\mathbb {Z} )^{\times },\{1,\circ \})}
54:
50:
1704:
1668:
1648:
57:
432:
The Vedic Square can be viewed as the multiplication table of the
1522:
1770:
Shanti Swarup
Bhatnagar Prize recipients in Mathematical Science
1512:
1384:, Great Britain: Cambridge University Press, pp. 119ā122,
1285:
433:
1206:
1169:
36:
1400:
The
Mystery of Numbers: Revealed Through Their Digital Root
1971:
Infinite series expansions for the trigonometric functions
1164:
746:
because not every non-zero element has a corresponding
49:
of the product of the column and row headings i.e. the
1259:{\displaystyle (a\times b)\mod {({\textrm {base}}-1)}}
2220:
Ramanujan
Institute for Advanced Study in Mathematics
1965:
1215:
988:
943:
872:
832:
788:
756:
704:
678:
606:
580:
556:
513:
441:
92:
1432:, Recreational Mathematics Magazine, pp. 9ā31,
542:is the set of positive integers partitioned by the
1340:"Digital root patterns of three-dimensional space"
1307:"Digital Root Patterns of Three-Dimensional Space"
1258:
1192:
994:
964:
914:
850:
818:
774:
731:
690:
664:
592:
562:
534:
499:
98:
41:is a variation on a typical 9 × 9
2237:
1429:Digital Root Patterns of Three-Dimensional Space
1201:Vedic square in base 100 (left) and 1000 (right)
1181:A Vedic cube is defined as the layout of each
1459:
1402:, CreateSpace Publications, pp. 68ā73,
909:
873:
813:
795:
656:
644:
491:
479:
1987:Kerala school of astronomy and mathematics
1466:
1452:
965:{\displaystyle \mathbb {Z} /9\mathbb {Z} }
535:{\displaystyle \mathbb {Z} /9\mathbb {Z} }
27:Multiplication table in Indian mathematics
1379:
1322:
1236:
1235:
958:
945:
725:
724:
627:
614:
528:
515:
462:
449:
2215:Homi Bhabha Centre for Science Education
1196:
1168:
861:
70:
1425:
1415:
1397:
1361:
1165:From two dimensions to three dimensions
427:
14:
2238:
1473:
930:- this is the group of multiplicative
1447:
1366:, New York: Dover, pp. 162ā167,
819:{\displaystyle a\in \{1,\cdots ,9\}}
45:where the entry in each cell is the
1740:Subbayya Sivasankaranarayana Pillai
1304:
732:{\displaystyle (a\times b)\mod {9}}
24:
2200:Institute of Mathematical Sciences
25:
2262:
2210:Harish-Chandra Research Institute
1720:K. R. Parthasarathy (probabilist)
1311:Recreational Mathematics Magazine
1337:
1231:
1193:Vedic squares in a higher radix
915:{\displaystyle \{1,2,4,5,7,8\}}
720:
2195:Chennai Mathematical Institute
1564:Melpathur Narayana Bhattathiri
1331:
1298:
1253:
1237:
1228:
1216:
717:
705:
659:
632:
610:
607:
494:
467:
445:
442:
13:
1:
1291:
978:
82:
2185:Indian Statistical Institute
1205:Vedic squares with a higher
7:
2205:Indian Institute of Science
2190:Bhaskaracharya Pratishthana
2068:A. A. Krishnaswamy Ayyangar
2033:Shankar Balakrishna Dikshit
1960:HinduāArabic numeral system
1269:
979:
851:{\displaystyle 9\circ a=6.}
83:
10:
2267:
1700:Subrahmanyan Chandrasekhar
1419:Digital Root: Vedic Square
775:{\displaystyle 6\circ 3=9}
2175:
2139:
2113:
2017:
1979:
1945:
1782:
1710:Veeravalli S. Varadarajan
1677:
1536:
1490:
1481:
1380:Pritchard, Chris (2003),
2126:Henry Thomas Colebrooke
1715:S. R. Srinivasa Varadhan
926:with 2 as one choice of
691:{\displaystyle a\circ b}
1599:MÄdhava of Saį¹
gamagrÄma
1398:Ghannam, Talal (2012),
1185:in a three-dimensional
1416:Teknomo, Kadi (2005),
1362:Deskins, W.E. (1996),
1344:rmm.ludus-opuscula.org
1260:
1202:
1178:
996:
995:{\displaystyle \circ }
966:
916:
852:
820:
776:
733:
692:
666:
594:
564:
563:{\displaystyle \circ }
536:
501:
100:
99:{\displaystyle \circ }
80:
1810:BrÄhmasphuį¹asiddhÄnta
1426:Chia-Yu, Lin (2016),
1324:10.1515/rmm-2016-0002
1305:Lin, Chia-Yu (2016).
1261:
1200:
1172:
997:
967:
917:
862:Properties of subsets
853:
821:
777:
742:This does not form a
734:
693:
667:
595:
565:
537:
502:
101:
74:
2086:T. A. Saraswati Amma
1797:Bakhshali manuscript
1765:Kannan Soundararajan
1213:
1187:multiplication table
986:
941:
870:
830:
786:
754:
702:
676:
604:
578:
554:
549:nine. (the operator
511:
439:
428:Algebraic properties
90:
43:multiplication table
2162:Islamic mathematics
2121:Walter Eugene Clark
1915:Vasishtha Siddhanta
1887:SiddhÄnta Shiromani
1866:Paitamaha Siddhanta
1745:Tilak Raj Prabhakar
1690:Satyendra Nath Bose
1685:Srinivasa Ramanujan
1639:Nilakantha Somayaji
593:{\displaystyle a,b}
77:reflection symmetry
2251:Modular arithmetic
2246:Indian mathematics
1654:Gangesha Upadhyaya
1475:Indian mathematics
1281:Modular arithmetic
1256:
1203:
1179:
992:
962:
912:
848:
816:
772:
729:
698:can be defined as
688:
662:
590:
560:
532:
497:
96:
81:
32:Indian mathematics
2233:
2232:
2039:Sudhakara Dvivedi
1859:Paulisa Siddhanta
1778:
1777:
1634:Jagannatha Samrat
1629:Achyuta Pisharati
1409:978-1-4776-7841-1
1244:
1161:
1160:
424:
423:
16:(Redirected from
2258:
1873:Romaka Siddhanta
1755:Akshay Venkatesh
1725:M. S. Narasimhan
1695:P.C. Mahalanobis
1488:
1487:
1468:
1461:
1454:
1445:
1444:
1440:
1422:
1412:
1394:
1376:
1364:Abstract Algebra
1354:
1353:
1351:
1350:
1335:
1329:
1328:
1326:
1302:
1265:
1263:
1262:
1257:
1246:
1245:
1242:
1177:(lower figures)
1001:
999:
998:
993:
980:
971:
969:
968:
963:
961:
953:
948:
921:
919:
918:
913:
857:
855:
854:
849:
825:
823:
822:
817:
782:but there is no
781:
779:
778:
773:
738:
736:
735:
730:
697:
695:
694:
689:
671:
669:
668:
663:
640:
639:
630:
622:
617:
600:are elements of
599:
597:
596:
591:
569:
567:
566:
561:
541:
539:
538:
533:
531:
523:
518:
506:
504:
503:
498:
475:
474:
465:
457:
452:
105:
103:
102:
97:
84:
21:
2266:
2265:
2261:
2260:
2259:
2257:
2256:
2255:
2236:
2235:
2234:
2229:
2177:
2171:
2135:
2109:
2080:C. T. Rajagopal
2027:Bapudeva Sastri
2019:
2013:
1975:
1955:Brahmi numerals
1947:
1941:
1901:Surya Siddhanta
1774:
1750:Manjul Bhargava
1673:
1532:
1477:
1472:
1410:
1392:
1374:
1358:
1357:
1348:
1346:
1336:
1332:
1303:
1299:
1294:
1272:
1241:
1240:
1214:
1211:
1210:
1195:
1167:
1162:
987:
984:
983:
957:
949:
944:
942:
939:
938:
871:
868:
867:
864:
831:
828:
827:
787:
784:
783:
755:
752:
751:
750:; for example
748:inverse element
703:
700:
699:
677:
674:
673:
635:
631:
626:
618:
613:
605:
602:
601:
579:
576:
575:
555:
552:
551:
544:residue classes
527:
519:
514:
512:
509:
508:
470:
466:
461:
453:
448:
440:
437:
436:
430:
425:
91:
88:
87:
28:
23:
22:
15:
12:
11:
5:
2264:
2254:
2253:
2248:
2231:
2230:
2228:
2227:
2222:
2217:
2212:
2207:
2202:
2197:
2192:
2187:
2181:
2179:
2173:
2172:
2170:
2169:
2164:
2159:
2154:
2149:
2143:
2141:
2137:
2136:
2134:
2133:
2128:
2123:
2117:
2115:
2111:
2110:
2108:
2107:
2101:
2095:
2089:
2083:
2077:
2071:
2065:
2060:
2054:
2051:P. C. Sengupta
2048:
2042:
2036:
2030:
2023:
2021:
2015:
2014:
2012:
2011:
1989:
1983:
1981:
1977:
1976:
1974:
1973:
1968:
1962:
1957:
1951:
1949:
1943:
1942:
1940:
1939:
1932:
1925:
1918:
1911:
1908:Tantrasamgraha
1904:
1897:
1890:
1883:
1876:
1869:
1862:
1855:
1848:
1841:
1834:
1831:Karanapaddhati
1827:
1820:
1817:Ganita Kaumudi
1813:
1806:
1799:
1794:
1786:
1784:
1780:
1779:
1776:
1775:
1773:
1772:
1767:
1762:
1757:
1752:
1747:
1742:
1737:
1735:Harish-Chandra
1732:
1730:C. S. Seshadri
1727:
1722:
1717:
1712:
1707:
1702:
1697:
1692:
1687:
1681:
1679:
1675:
1674:
1672:
1671:
1666:
1664:Sankara Variar
1661:
1656:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1581:
1576:
1571:
1566:
1561:
1556:
1551:
1546:
1540:
1538:
1534:
1533:
1531:
1530:
1525:
1520:
1515:
1510:
1505:
1500:
1494:
1492:
1485:
1483:Mathematicians
1479:
1478:
1471:
1470:
1463:
1456:
1448:
1442:
1441:
1423:
1413:
1408:
1395:
1390:
1377:
1372:
1356:
1355:
1338:Lin, Chia-Yu.
1330:
1296:
1295:
1293:
1290:
1289:
1288:
1283:
1278:
1271:
1268:
1255:
1252:
1249:
1239:
1234:
1230:
1227:
1224:
1221:
1218:
1194:
1191:
1166:
1163:
1159:
1158:
1155:
1152:
1149:
1146:
1143:
1140:
1136:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1113:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1090:
1089:
1086:
1083:
1080:
1077:
1074:
1071:
1067:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1044:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1021:
1020:
1017:
1014:
1011:
1008:
1005:
1002:
991:
960:
956:
952:
947:
911:
908:
905:
902:
899:
896:
893:
890:
887:
884:
881:
878:
875:
863:
860:
847:
844:
841:
838:
835:
815:
812:
809:
806:
803:
800:
797:
794:
791:
771:
768:
765:
762:
759:
728:
723:
719:
716:
713:
710:
707:
687:
684:
681:
661:
658:
655:
652:
649:
646:
643:
638:
634:
629:
625:
621:
616:
612:
609:
589:
586:
583:
559:
530:
526:
522:
517:
496:
493:
490:
487:
484:
481:
478:
473:
469:
464:
460:
456:
451:
447:
444:
429:
426:
422:
421:
418:
415:
412:
409:
406:
403:
400:
397:
394:
390:
389:
386:
383:
380:
377:
374:
371:
368:
365:
362:
358:
357:
354:
351:
348:
345:
342:
339:
336:
333:
330:
326:
325:
322:
319:
316:
313:
310:
307:
304:
301:
298:
294:
293:
290:
287:
284:
281:
278:
275:
272:
269:
266:
262:
261:
258:
255:
252:
249:
246:
243:
240:
237:
234:
230:
229:
226:
223:
220:
217:
214:
211:
208:
205:
202:
198:
197:
194:
191:
188:
185:
182:
179:
176:
173:
170:
166:
165:
162:
159:
156:
153:
150:
147:
144:
141:
138:
134:
133:
130:
127:
124:
121:
118:
115:
112:
109:
106:
95:
26:
9:
6:
4:
3:
2:
2263:
2252:
2249:
2247:
2244:
2243:
2241:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2182:
2180:
2174:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2148:
2145:
2144:
2142:
2140:Other regions
2138:
2132:
2131:David Pingree
2129:
2127:
2124:
2122:
2119:
2118:
2116:
2112:
2105:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2072:
2069:
2066:
2064:
2061:
2058:
2055:
2052:
2049:
2046:
2045:M. Rangacarya
2043:
2040:
2037:
2034:
2031:
2028:
2025:
2024:
2022:
2018:Historians of
2016:
2009:
2005:
2001:
1997:
1993:
1992:Jantar Mantar
1990:
1988:
1985:
1984:
1982:
1978:
1972:
1969:
1967:
1963:
1961:
1958:
1956:
1953:
1952:
1950:
1944:
1938:
1937:
1933:
1931:
1930:
1926:
1924:
1923:
1919:
1917:
1916:
1912:
1910:
1909:
1905:
1903:
1902:
1898:
1896:
1895:
1891:
1889:
1888:
1884:
1882:
1881:
1877:
1875:
1874:
1870:
1868:
1867:
1863:
1861:
1860:
1856:
1854:
1853:
1849:
1847:
1846:
1842:
1840:
1839:
1835:
1833:
1832:
1828:
1826:
1825:
1821:
1819:
1818:
1814:
1812:
1811:
1807:
1805:
1804:
1800:
1798:
1795:
1793:
1792:
1788:
1787:
1785:
1781:
1771:
1768:
1766:
1763:
1761:
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1706:
1703:
1701:
1698:
1696:
1693:
1691:
1688:
1686:
1683:
1682:
1680:
1676:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1609:Mahendra SÅ«ri
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1590:
1587:
1585:
1582:
1580:
1577:
1575:
1572:
1570:
1567:
1565:
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1541:
1539:
1535:
1529:
1526:
1524:
1521:
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2178:institutions
2098:K. S. Shukla
2070:(1892ā 1953)
1936:Yavanajataka
1934:
1927:
1920:
1913:
1906:
1899:
1894:Åulba SÅ«tras
1892:
1885:
1880:Sadratnamala
1878:
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1864:
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1850:
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1836:
1829:
1824:Kanakkusaram
1822:
1815:
1808:
1801:
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1659:VarÄhamihira
1624:Parameshvara
1579:GovindasvÄmi
1549:Äryabhaį¹a II
1428:
1418:
1399:
1381:
1363:
1347:. Retrieved
1343:
1333:
1314:
1310:
1300:
1276:Latin square
1204:
1183:digital root
1180:
1174:
974:Latin square
924:cyclic group
865:
741:
573:
550:
431:
47:digital root
35:
29:
18:Vedic Square
2114:Translators
2106:(1919ā2005)
2104:K. V. Sarma
2100:(1918ā2007)
2094:(1918ā1992)
2088:(1918ā2000)
2082:(1903ā1978)
2076:(1901ā1954)
2074:A. N. Singh
2059:(1888ā1958)
2057:B. B. Datta
2053:(1876ā1962)
2047:(1861ā1916)
2041:(1855ā1910)
2035:(1853ā1898)
2029:(1821ā1900)
2020:mathematics
1964:Symbol for
1948:innovations
1845:Lokavibhaga
1791:Aryabhatiya
1589:Jyeį¹£į¹hadeva
1574:Brahmagupta
1559:BhÄskara II
1544:Äryabhaį¹a I
1528:Yajnavalkya
1317:(5): 9ā31.
866:The subset
66:Islamic art
2240:Categories
2063:T. Hayashi
1946:Pioneering
1929:YuktibhÄį¹£Ä
1852:PÄtÄ«gaį¹ita
1803:Bijaganita
1760:Ravi Vakil
1614:Munishvara
1594:Kamalakara
1569:Brahmadeva
1554:BhÄskara I
1503:Baudhayana
1349:2016-05-25
1292:References
826:such that
62:symmetries
2092:S. N. Sen
2000:New Delhi
1922:Veį¹vÄroha
1783:Treatises
1584:Halayudha
1537:Classical
1508:Katyayana
1498:Apastamba
1438:2182-1976
1248:−
1223:×
990:∘
928:generator
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793:∈
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712:×
683:∘
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637:×
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51:remainder
2008:Varanasi
1966:zero (0)
1838:LÄ«lÄvatÄ«
1705:C.R. Rao
1669:Virasena
1649:Sridhara
1619:Narayana
1604:MahÄvÄ«ra
1270:See also
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58:patterns
2147:Babylon
1980:Centres
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1523:Pingala
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2176:Modern
2167:Europe
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2004:Ujjain
1996:Jaipur
1678:Modern
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547:modulo
507:where
434:monoid
39:square
2152:China
1207:radix
932:units
744:group
672:then
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2225:TIFR
1434:ISSN
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