1981:
2053:
2017:
1969:
2041:
1993:
2029:
2005:
1957:
362:
written in verses. Bhāskara's comments referred exactly to the 33 verses dealing with mathematics, in which he considered variable equations and trigonometric formulae. In general, he emphasized proving mathematical rules instead of simply relying on tradition or expediency.
286:. The first positional representations had been known to Indian astronomers approximately 500 years before Bhāskara's work. However, these numbers were written not in figures, but in words or allegories and were organized in verses. For instance, the number 1 was given as
495:
314:
Bhāskara's numeral system was truly positional, in contrast to word representations, where the same word could represent multiple values (such as 40 or 400). He often explained a number given in his numeral system by stating
310:
system, these words were aligned such that each number assigns the factor of the power of ten corresponding to its position, only in reverse order: the higher powers were to the right of the lower ones.
545:
573:). Additionally, he gives relations between sine and cosine, as well as relations between the sine of an angle less than 90° and the sines of angles 90°–180°, 180°–270°, and greater than 270°.
682:
relative to pell's equation). This equation has the simple solution x = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions can be constructed, such as (x,y) = (6,17).
1777:
1742:
680:
631:
723:
380:
327:. Contrary to the word system, however, his numerals were written in descending values from left to right, exactly as we do it today. Therefore, since at least 629, the
571:
1929:
1479:
216:
Little is known about Bhāskara's life, except for what can be deduced from his writings. He was born in India in the 7th century, and was probably an
1754:
776:
371:
112:
1175:
1909:
1801:
2073:
1696:
809:
748:
consists of eight chapters dealing with mathematical astronomy. The book deals with topics such as the longitudes of the planets, the
1871:
1115:
Expounding the
Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhāskara I on the Mathematical Chapter of the Aryabhatiya
1096:
Expounding the
Mathematical Seed. Vol. 1: The Translation: A Translation of Bhāskara I on the Mathematical Chapter of the Aryabhatiya
1924:
2078:
1142:
1934:
331:
system was definitely known to Indian scholars. Presumably, Bhāskara did not invent it, but he was the first to openly use the
1876:
2098:
503:
1449:
2103:
1919:
1429:
1122:
1103:
1088:
1074:
1059:
274:
are two of the most renowned Indian mathematicians; both made considerable contributions to the study of fractions.
2088:
1168:
1017:
Mahābhāskarīya of Bhāskarācārya with the Bhāṣya of
Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara
1669:
154:
2093:
1904:
1519:
1273:
1313:
1192:
1031:
Laghubhāskarīya, Edited and
Translated into English, with Explanatory and Critical Notes, and Comments, etc.,
786:
582:
Tell me, O mathematician, what is that square which multiplied by 8 becomes – together with unity – a square?
1894:
1024:
Mahābhāskarīya, Edited and
Translated into English, with Explanatory and Critical Notes, and Comments, etc.
2083:
1914:
1899:
1161:
914:
1947:
1409:
282:
The most important mathematical contribution of Bhāskara I concerns the representation of numbers in a
1419:
500:
which he assigns to
Aryabhata. It reveals a relative error of less than 1.9% (the greatest deviation
283:
20:
1137:
636:
587:
1709:
1575:
1424:
1147:
490:{\displaystyle \sin x\approx {\frac {16x(\pi -x)}{5\pi ^{2}-4x(\pi -x)}},\qquad (0\leq x\leq \pi )}
704:
1835:
1717:
1308:
749:
841:
1856:
1783:
1596:
1713:
1705:
1207:
1795:
1506:
1474:
354:
205:
8:
2045:
1861:
1830:
1638:
1624:
1561:
1454:
1399:
1394:
1348:
1298:
1133:
781:
550:
256:
236:
51:
2033:
2021:
1985:
1363:
1184:
577:
2108:
1980:
1866:
1748:
1568:
1343:
1338:
1212:
1118:
1099:
1084:
1070:
1055:
1050:
H.-W. Alten, A. Djafari Naini, M. Folkerts, H. Schlosser, K.-H. Schlote, H. Wußing:
370:
is divided into eight chapters about mathematical astronomy. In chapter 7, he gives
1997:
1961:
1582:
1464:
1434:
1404:
232:
1547:
1318:
877:
1789:
1736:
1664:
1610:
1459:
1328:
576:
Moreover, Bhāskara stated theorems about the solutions to equations now known as
1368:
1288:
2057:
1760:
1680:
1617:
1540:
1526:
1444:
1439:
1373:
1217:
332:
320:
1268:
848:. School of Mathematics and Statistics, University of St Andrews, Scotland, UK
189:. He also wrote two astronomical works in the line of Aryabhata's school: the
142:
2067:
1840:
1772:
1701:
1603:
942:
733:
319:("in figures this reads"), and then repeating it written with the first nine
162:
139:
1227:
972:
960:
Erwachende
Wissenschaft. Ägyptische, babylonische und griechische Mathematik
352:
Bhāskara I wrote three astronomical contributions. In 629, he annotated the
2009:
1973:
1807:
1645:
1589:
1533:
1353:
1333:
1258:
1813:
1766:
1554:
1500:
1283:
1237:
1038:Āryabhaṭīya of Āryabhaṭa, with the commentary of Bhāskara I and Someśvara
271:
182:
84:
227:
There are references to places in India in Bhāskara's writings, such as
1512:
1469:
1323:
1303:
1278:
324:
217:
158:
146:
2052:
584:" In modern notation, he asked for the solutions of the Pell equation
1631:
1293:
1253:
1153:
752:
among the planets and stars, the phases of the moon, solar and lunar
694:
359:
267:
221:
186:
170:
80:
302:
since they always occur in pairs; the number 5 was given by the (5)
260:
76:
55:
1414:
1378:
1358:
336:
255:. Therefore, a reasonable guess would be that Bhāskara was born in
248:
228:
178:
1033:
Department of mathematics and astronomy, Lucknow
University, 2012.
1232:
753:
726:
328:
307:
244:
240:
1480:
Shanti Swarup
Bhatnagar Prize recipients in Mathematical Science
1222:
816:. Complete Dictionary of Scientific Biography. 30 November 2022
764:
252:
235:
in the 7th century) and
Sivarajapura, both of which are in the
150:
290:, since it exists only once; the number 2 was represented by
1117:, Basel, Boston, and Berlin: Birkhäuser Verlag, 206 pages,
1098:, Basel, Boston, and Berlin: Birkhäuser Verlag, 172 pages,
1040:. Indian National Science Academy (INSA), New- Delhi, 1999.
201:
177:, written in 629, is among the oldest known prose works in
166:
2004:
1681:
Infinite series expansions for the trigonometric functions
973:"Bhāskara i | Famous Indian Mathematician and Astronomer"
1010:
The Laghubhāskarīya, with the commentary of Parameśvara
686:
266:
Bhāskara I is considered the most important scholar of
1945:
1930:
Ramanujan Institute for Advanced Study in Mathematics
1675:
707:
639:
590:
553:
506:
383:
1026:
Department of mathematics, Lucknow University, 1960.
1012:. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
540:{\displaystyle {\frac {16}{5\pi }}-1\approx 1.859\%}
1065:S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (Hrsg.):
717:
674:
625:
565:
539:
489:
1131:
839:
732:He was the first mathematician to openly discuss
2065:
161:, and who gave a unique and remarkable rational
1019:. Madras Govt. Oriental series, no. cxxx, 1957.
1169:
962:. Birkäuser-Verlag Basel Stuttgart 1966 p. 90
756:, and the rising and setting of the planets.
145:) was a 7th-century Indian mathematician and
16:Indian mathematician and astronomer (600-680)
372:a remarkable approximation formula for sin x
277:
919:Nasa Space Science Data Coordinated Archive
1697:Kerala school of astronomy and mathematics
1176:
1162:
1069:. Verlag Harri Thun, Frankfurt a. M. 1990
251:in the eastern Punjab, which was ruled by
138:to avoid confusion with the 12th-century
1925:Homi Bhabha Centre for Science Education
947:Census of the Exact Sciences in Sanskrit
342:
208:, named in honour of the mathematician.
1143:MacTutor History of Mathematics Archive
1112:
1093:
1083:. John Wiley & Sons, New York 2000
1054:Springer-Verlag Berlin Heidelberg 2003
1001:
938:
901:
875:
777:Bhāskara I's sine approximation formula
580:. For instance, he posed the problem: "
113:Bhāskara I's sine approximation formula
2066:
1183:
736:with four unequal, nonparallel sides.
1157:
701:, he criticized its approximation to
871:
869:
867:
865:
863:
835:
833:
831:
804:
802:
1450:Subbayya Sivasankaranarayana Pillai
239:region of the present-day state of
193:("Great Book of Bhāskara") and the
19:For others with the same name, see
13:
1910:Institute of Mathematical Sciences
1044:
840:O'Connor, J. J.; Robertson, E. F.
534:
202:Indian Space Research Organisation
14:
2120:
2074:7th-century Indian mathematicians
1920:Harish-Chandra Research Institute
1430:K. R. Parthasarathy (probabilist)
860:
828:
799:
2051:
2039:
2027:
2015:
2003:
1991:
1979:
1967:
1955:
1081:The Universal History of Numbers
1067:Lexikon bedeutender Mathematiker
335:in a scientific contribution in
685:Bhāskara clearly believed that
465:
323:, using a small circle for the
270:'s astronomical school. He and
2079:7th-century Indian astronomers
1905:Chennai Mathematical Institute
1274:Melpathur Narayana Bhattathiri
965:
952:
932:
907:
895:
876:Hayashi, Takao (1 July 2019).
693:was irrational. In support of
675:{\displaystyle y^{2}-8x^{2}=1}
626:{\displaystyle 8x^{2}+1=y^{2}}
484:
466:
456:
444:
417:
405:
358:, an astronomical treatise by
347:
169:function in his commentary on
1:
792:
787:List of Indian mathematicians
243:in India. Also mentioned are
124:
66:
41:
1895:Indian Statistical Institute
941:, p. xiii) cites , and
739:
718:{\displaystyle {\sqrt {10}}}
211:
197:("Small Book of Bhāskara").
7:
2099:Scientists from Maharashtra
1915:Indian Institute of Science
1900:Bhaskaracharya Pratishthana
1778:A. A. Krishnaswamy Ayyangar
1743:Shankar Balakrishna Dikshit
1670:Hindu–Arabic numeral system
770:
763:were later translated into
224:education from his father.
155:Hindu–Arabic decimal system
149:who was the first to write
10:
2125:
1410:Subrahmanyan Chandrasekhar
995:
725:, a practice common among
220:. Bhāskara I received his
173:'s work. This commentary,
18:
2104:Scholars from Maharashtra
1885:
1849:
1823:
1727:
1689:
1655:
1492:
1420:Veeravalli S. Varadarajan
1387:
1246:
1200:
1191:
306:. Similar to our current
284:positional numeral system
278:Representation of numbers
247:in southern Gujarat, and
108:
100:
92:
62:
37:
30:
21:Bhaskara (disambiguation)
1836:Henry Thomas Colebrooke
1425:S. R. Srinivasa Varadhan
1148:University of St Andrews
1113:Keller, Agathe (2006b),
1094:Keller, Agathe (2006a),
842:"Bhāskara I – Biography"
104:Mathematician, scientist
2089:Scientists from Gujarat
1309:Mādhava of Saṅgamagrāma
882:Encyclopedia Britannica
719:
676:
627:
567:
541:
491:
157:with a circle for the
2094:Scholars from Gujarat
1520:Brāhmasphuṭasiddhānta
720:
677:
628:
568:
542:
492:
343:Further contributions
1796:T. A. Saraswati Amma
1507:Bakhshali manuscript
1475:Kannan Soundararajan
1134:Robertson, Edmund F.
958:B. van der Waerden:
705:
697:'s approximation of
637:
588:
551:
504:
381:
231:(the capital of the
206:Bhāskara I satellite
200:On 7 June 1979, the
1872:Islamic mathematics
1831:Walter Eugene Clark
1625:Vasishtha Siddhanta
1597:Siddhānta Shiromani
1576:Paitamaha Siddhanta
1455:Tilak Raj Prabhakar
1400:Satyendra Nath Bose
1395:Srinivasa Ramanujan
1349:Nilakantha Somayaji
1132:O'Connor, John J.;
1052:4000 Jahre Algebra.
979:. 28 September 2020
949:, volume 4, p. 297.
782:List of astronomers
566:{\displaystyle x=0}
259:and later moved to
134:) (commonly called
2084:7th-century deaths
1364:Gangesha Upadhyaya
1185:Indian mathematics
715:
672:
623:
563:
537:
487:
1943:
1942:
1749:Sudhakara Dvivedi
1569:Paulisa Siddhanta
1488:
1487:
1344:Jagannatha Samrat
1339:Achyuta Pisharati
1004:, p. xiii))
729:mathematicians.
713:
520:
460:
175:Āryabhaṭīyabhāṣya
118:
117:
2116:
2056:
2055:
2044:
2043:
2042:
2032:
2031:
2030:
2020:
2019:
2018:
2008:
2007:
1996:
1995:
1994:
1984:
1983:
1972:
1971:
1970:
1960:
1959:
1958:
1951:
1583:Romaka Siddhanta
1465:Akshay Venkatesh
1435:M. S. Narasimhan
1405:P.C. Mahalanobis
1198:
1197:
1178:
1171:
1164:
1155:
1154:
1150:
1127:
1108:
989:
988:
986:
984:
969:
963:
956:
950:
936:
930:
929:
927:
925:
911:
905:
899:
893:
892:
890:
888:
873:
858:
857:
855:
853:
837:
826:
825:
823:
821:
814:Encyclopedia.com
806:
724:
722:
721:
716:
714:
709:
700:
690:
681:
679:
678:
673:
665:
664:
649:
648:
632:
630:
629:
624:
622:
621:
603:
602:
578:Pell's equations
572:
570:
569:
564:
546:
544:
543:
538:
521:
519:
508:
496:
494:
493:
488:
461:
459:
434:
433:
420:
397:
233:Maitraka dynasty
133:
129:
126:
71:
68:
46:
43:
28:
27:
2124:
2123:
2119:
2118:
2117:
2115:
2114:
2113:
2064:
2063:
2062:
2050:
2040:
2038:
2028:
2026:
2016:
2014:
2002:
1992:
1990:
1978:
1968:
1966:
1956:
1954:
1946:
1944:
1939:
1887:
1881:
1845:
1819:
1790:C. T. Rajagopal
1737:Bapudeva Sastri
1729:
1723:
1685:
1665:Brahmi numerals
1657:
1651:
1611:Surya Siddhanta
1484:
1460:Manjul Bhargava
1383:
1242:
1187:
1182:
1125:
1106:
1047:
1045:Further reading
998:
993:
992:
982:
980:
971:
970:
966:
957:
953:
937:
933:
923:
921:
913:
912:
908:
904:, p. xiii)
900:
896:
886:
884:
874:
861:
851:
849:
838:
829:
819:
817:
808:
807:
800:
795:
773:
742:
708:
706:
703:
702:
698:
688:
660:
656:
644:
640:
638:
635:
634:
617:
613:
598:
594:
589:
586:
585:
552:
549:
548:
512:
507:
505:
502:
501:
429:
425:
421:
398:
396:
382:
379:
378:
350:
345:
333:Brahmi numerals
321:Brahmi numerals
280:
214:
195:Laghubhāskarīya
131:
127:
88:
73:
69:
58:
48:
44:
33:
24:
17:
12:
11:
5:
2122:
2112:
2111:
2106:
2101:
2096:
2091:
2086:
2081:
2076:
2061:
2060:
2048:
2036:
2024:
2012:
2000:
1988:
1976:
1964:
1941:
1940:
1938:
1937:
1932:
1927:
1922:
1917:
1912:
1907:
1902:
1897:
1891:
1889:
1883:
1882:
1880:
1879:
1874:
1869:
1864:
1859:
1853:
1851:
1847:
1846:
1844:
1843:
1838:
1833:
1827:
1825:
1821:
1820:
1818:
1817:
1811:
1805:
1799:
1793:
1787:
1781:
1775:
1770:
1764:
1761:P. C. Sengupta
1758:
1752:
1746:
1740:
1733:
1731:
1725:
1724:
1722:
1721:
1699:
1693:
1691:
1687:
1686:
1684:
1683:
1678:
1672:
1667:
1661:
1659:
1653:
1652:
1650:
1649:
1642:
1635:
1628:
1621:
1618:Tantrasamgraha
1614:
1607:
1600:
1593:
1586:
1579:
1572:
1565:
1558:
1551:
1544:
1541:Karanapaddhati
1537:
1530:
1527:Ganita Kaumudi
1523:
1516:
1509:
1504:
1496:
1494:
1490:
1489:
1486:
1485:
1483:
1482:
1477:
1472:
1467:
1462:
1457:
1452:
1447:
1445:Harish-Chandra
1442:
1440:C. S. Seshadri
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1391:
1389:
1385:
1384:
1382:
1381:
1376:
1374:Sankara Variar
1371:
1366:
1361:
1356:
1351:
1346:
1341:
1336:
1331:
1326:
1321:
1316:
1311:
1306:
1301:
1296:
1291:
1286:
1281:
1276:
1271:
1266:
1261:
1256:
1250:
1248:
1244:
1243:
1241:
1240:
1235:
1230:
1225:
1220:
1215:
1210:
1204:
1202:
1195:
1193:Mathematicians
1189:
1188:
1181:
1180:
1173:
1166:
1158:
1152:
1151:
1129:
1123:
1110:
1104:
1091:
1077:
1063:
1046:
1043:
1042:
1041:
1036:K. S. Shukla.
1034:
1029:K. S. Shukla.
1027:
1022:K. S. Shukla.
1020:
1013:
997:
994:
991:
990:
964:
951:
931:
906:
894:
859:
827:
797:
796:
794:
791:
790:
789:
784:
779:
772:
769:
761:Mahābhāskarīya
746:Mahābhāskarīya
741:
738:
734:quadrilaterals
712:
671:
668:
663:
659:
655:
652:
647:
643:
620:
616:
612:
609:
606:
601:
597:
593:
562:
559:
556:
536:
533:
530:
527:
524:
518:
515:
511:
498:
497:
486:
483:
480:
477:
474:
471:
468:
464:
458:
455:
452:
449:
446:
443:
440:
437:
432:
428:
424:
419:
416:
413:
410:
407:
404:
401:
395:
392:
389:
386:
368:Mahābhāskarīya
349:
346:
344:
341:
279:
276:
213:
210:
191:Mahābhāskarīya
116:
115:
110:
109:Known for
106:
105:
102:
98:
97:
94:
90:
89:
74:
64:
60:
59:
49:
39:
35:
34:
31:
15:
9:
6:
4:
3:
2:
2121:
2110:
2107:
2105:
2102:
2100:
2097:
2095:
2092:
2090:
2087:
2085:
2082:
2080:
2077:
2075:
2072:
2071:
2069:
2059:
2054:
2049:
2047:
2037:
2035:
2025:
2023:
2013:
2011:
2006:
2001:
1999:
1989:
1987:
1982:
1977:
1975:
1965:
1963:
1953:
1952:
1949:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1916:
1913:
1911:
1908:
1906:
1903:
1901:
1898:
1896:
1893:
1892:
1890:
1884:
1878:
1875:
1873:
1870:
1868:
1865:
1863:
1860:
1858:
1855:
1854:
1852:
1850:Other regions
1848:
1842:
1841:David Pingree
1839:
1837:
1834:
1832:
1829:
1828:
1826:
1822:
1815:
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1124:3-7643-7292-3
1120:
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1105:3-7643-7291-5
1101:
1097:
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1089:0-471-39340-1
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1075:3-8171-1164-9
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1060:3-540-43554-9
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978:
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101:Occupation(s)
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79:(present-day
78:
65:
61:
57:
53:
40:
36:
29:
26:
22:
2046:Solar System
1888:institutions
1808:K. S. Shukla
1780:(1892– 1953)
1646:Yavanajataka
1644:
1637:
1630:
1623:
1616:
1609:
1604:Śulba Sūtras
1602:
1595:
1590:Sadratnamala
1588:
1581:
1574:
1567:
1560:
1553:
1546:
1539:
1534:Kanakkusaram
1532:
1525:
1518:
1511:
1499:
1369:Varāhamihira
1334:Parameshvara
1289:Govindasvāmi
1263:
1259:Āryabhaṭa II
1141:
1138:"Bhāskara I"
1114:
1095:
1080:
1066:
1051:
1037:
1030:
1023:
1016:
1009:
999:
981:. Retrieved
976:
967:
959:
954:
946:
934:
924:16 September
922:. Retrieved
918:
909:
897:
885:. Retrieved
881:
878:"Bhāskara I"
850:. Retrieved
845:
818:. Retrieved
813:
810:"Bhāskara I"
760:
758:
750:conjunctions
745:
743:
731:
687:
684:
581:
575:
499:
367:
365:
353:
351:
316:
313:
303:
299:
295:
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265:
226:
222:astronomical
215:
199:
194:
190:
174:
135:
120:
119:
25:
2034:Outer space
2022:Spaceflight
1986:Mathematics
1824:Translators
1816:(1919–2005)
1814:K. V. Sarma
1810:(1918–2007)
1804:(1918–1992)
1798:(1918–2000)
1792:(1903–1978)
1786:(1901–1954)
1784:A. N. Singh
1769:(1888–1958)
1767:B. B. Datta
1763:(1876–1962)
1757:(1861–1916)
1751:(1855–1910)
1745:(1853–1898)
1739:(1821–1900)
1730:mathematics
1674:Symbol for
1658:innovations
1555:Lokavibhaga
1501:Aryabhatiya
1299:Jyeṣṭhadeva
1284:Brahmagupta
1269:Bhāskara II
1254:Āryabhaṭa I
1238:Yajnavalkya
983:3 September
887:12 December
820:12 December
355:Āryabhaṭīya
348:Mathematics
272:Brahmagupta
183:mathematics
143:Bhāskara II
93:Nationality
85:Maharashtra
2068:Categories
1773:T. Hayashi
1656:Pioneering
1639:Yuktibhāṣā
1562:Pātīgaṇita
1513:Bijaganita
1470:Ravi Vakil
1324:Munishvara
1304:Kamalakara
1279:Brahmadeva
1264:Bhāskara I
1213:Baudhayana
1079:G. Ifrah:
915:"Bhāskara"
793:References
317:ankair api
218:astronomer
147:astronomer
136:Bhāskara I
132: 680
130: – c.
128: 600
70: 680
45: 600
32:Bhāskara I
1998:Astronomy
1962:Biography
1802:S. N. Sen
1710:New Delhi
1632:Veṇvāroha
1493:Treatises
1294:Halayudha
1247:Classical
1218:Katyayana
1208:Apastamba
1015:v.harish
759:Parts of
740:Astronomy
695:Aryabhata
651:−
535:%
529:≈
523:−
517:π
482:π
479:≤
473:≤
451:−
448:π
436:−
427:π
412:−
409:π
394:≈
388:
366:His work
360:Aryabhata
268:Aryabhata
257:Saurastra
237:Saurastra
212:Biography
187:astronomy
171:Aryabhata
81:Telangana
75:possibly
52:Saurāṣṭra
50:possibly
2109:Acharyas
1718:Varanasi
1676:zero (0)
1548:Līlāvatī
1415:C.R. Rao
1379:Virasena
1359:Sridhara
1329:Narayana
1314:Mahāvīra
1062:, §3.2.1
771:See also
754:eclipses
337:Sanskrit
249:Thanesar
229:Vallabhi
179:Sanskrit
121:Bhāskara
2058:Science
1948:Portals
1857:Babylon
1690:Centres
1354:Śrīpati
1233:Pingala
1201:Ancient
996:Sources
977:Cuemath
943:Pingree
329:decimal
308:decimal
245:Bharuch
241:Gujarat
165:of the
153:in the
151:numbers
1886:Modern
1877:Europe
1867:Greece
1714:Ujjain
1706:Jaipur
1388:Modern
1228:Pāṇini
1223:Manava
1121:
1102:
1087:
1073:
1058:
1000:(From
765:Arabic
304:senses
261:Aśmaka
253:Harsha
96:Indian
77:Aśmaka
56:Aśmaka
2010:Stars
1974:India
1862:China
852:5 May
532:1.859
298:, or
296:twins
292:wings
1935:TIFR
1119:ISBN
1100:ISBN
1085:ISBN
1071:ISBN
1056:ISBN
985:2022
926:2017
889:2022
854:2021
822:2022
744:The
727:Jain
633:(or
325:zero
300:eyes
288:moon
185:and
167:sine
159:zero
83:and
63:Died
38:Born
547:at
385:sin
181:on
54:or
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830:^
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