1992:
2064:
2028:
1980:
2052:
2004:
2040:
2016:
1968:
373:
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.
297:. 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
506:
325:
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
321:
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.
556:
584:). 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°.
693:
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).
1788:
1753:
691:
642:
734:
391:
338:. 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
582:
1940:
1490:
227:
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
1765:
787:
382:
123:
1186:
1920:
1812:
2084:
1707:
820:
759:
consists of eight chapters dealing with mathematical astronomy. The book deals with topics such as the longitudes of the planets, the
1882:
1126:
Expounding the
Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhāskara I on the Mathematical Chapter of the Aryabhatiya
1107:
Expounding the
Mathematical Seed. Vol. 1: The Translation: A Translation of Bhāskara I on the Mathematical Chapter of the Aryabhatiya
1935:
2089:
1153:
1945:
342:
system was definitely known to Indian scholars. Presumably, Bhāskara did not invent it, but he was the first to openly use the
1887:
2109:
514:
1460:
2114:
1930:
1440:
1133:
1114:
1099:
1085:
1070:
285:
are two of the most renowned Indian mathematicians; both made considerable contributions to the study of fractions.
2099:
1179:
1028:
Mahābhāskarīya of Bhāskarācārya with the Bhāṣya of
Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara
1680:
165:
2104:
1915:
1530:
1284:
1324:
1203:
1042:
Laghubhāskarīya, Edited and
Translated into English, with Explanatory and Critical Notes, and Comments, etc.,
797:
593:
Tell me, O mathematician, what is that square which multiplied by 8 becomes – together with unity – a square?
1905:
1035:
Mahābhāskarīya, Edited and
Translated into English, with Explanatory and Critical Notes, and Comments, etc.
2094:
1925:
1910:
1172:
925:
1958:
1420:
293:
The most important mathematical contribution of Bhāskara I concerns the representation of numbers in a
17:
1430:
511:
which he assigns to
Aryabhata. It reveals a relative error of less than 1.9% (the greatest deviation
294:
31:
1148:
647:
598:
1720:
1586:
1435:
1158:
501:{\displaystyle \sin x\approx {\frac {16x(\pi -x)}{5\pi ^{2}-4x(\pi -x)}},\qquad (0\leq x\leq \pi )}
715:
1846:
1728:
1319:
760:
852:
1867:
1794:
1607:
1724:
1716:
1218:
1806:
1517:
1485:
365:
216:
8:
2056:
1872:
1841:
1649:
1635:
1572:
1465:
1410:
1405:
1359:
1309:
1144:
792:
561:
267:
247:
62:
2044:
2032:
1996:
1374:
1195:
588:
2119:
1991:
1877:
1759:
1579:
1354:
1349:
1223:
1129:
1110:
1095:
1081:
1066:
1061:
H.-W. Alten, A. Djafari Naini, M. Folkerts, H. Schlosser, K.-H. Schlote, H. Wußing:
381:
is divided into eight chapters about mathematical astronomy. In chapter 7, he gives
2008:
1972:
1593:
1475:
1445:
1415:
243:
1558:
1329:
888:
1800:
1747:
1675:
1621:
1470:
1339:
587:
Moreover, Bhāskara stated theorems about the solutions to equations now known as
1379:
1299:
2068:
1771:
1691:
1628:
1551:
1537:
1455:
1450:
1384:
1228:
343:
331:
1279:
859:. School of Mathematics and Statistics, University of St Andrews, Scotland, UK
200:. He also wrote two astronomical works in the line of Aryabhata's school: the
153:
2078:
1851:
1783:
1712:
1614:
953:
744:
330:("in figures this reads"), and then repeating it written with the first nine
173:
150:
1238:
983:
971:
Erwachende
Wissenschaft. Ägyptische, babylonische und griechische Mathematik
363:
Bhāskara I wrote three astronomical contributions. In 629, he annotated the
2020:
1984:
1818:
1656:
1600:
1544:
1364:
1344:
1269:
1824:
1777:
1565:
1511:
1294:
1248:
1049:Āryabhaṭīya of Āryabhaṭa, with the commentary of Bhāskara I and Someśvara
282:
193:
95:
238:
There are references to places in India in Bhāskara's writings, such as
1523:
1480:
1334:
1314:
1289:
335:
228:
169:
157:
2063:
595:" In modern notation, he asked for the solutions of the Pell equation
1642:
1304:
1264:
1164:
763:
among the planets and stars, the phases of the moon, solar and lunar
705:
370:
278:
232:
197:
181:
91:
313:
since they always occur in pairs; the number 5 was given by the (5)
271:
87:
66:
1425:
1389:
1369:
347:
266:. Therefore, a reasonable guess would be that Bhāskara was born in
259:
239:
189:
1044:
Department of mathematics and astronomy, Lucknow
University, 2012.
1243:
764:
737:
339:
318:
255:
251:
1491:
Shanti Swarup
Bhatnagar Prize recipients in Mathematical Science
1233:
827:. Complete Dictionary of Scientific Biography. 30 November 2022
775:
263:
246:
in the 7th century) and
Sivarajapura, both of which are in the
161:
301:, since it exists only once; the number 2 was represented by
1128:, Basel, Boston, and Berlin: Birkhäuser Verlag, 206 pages,
1109:, Basel, Boston, and Berlin: Birkhäuser Verlag, 172 pages,
1051:. Indian National Science Academy (INSA), New- Delhi, 1999.
212:
188:, written in 629, is among the oldest known prose works in
177:
2015:
1692:
Infinite series expansions for the trigonometric functions
984:"Bhāskara i | Famous Indian Mathematician and Astronomer"
1021:
The Laghubhāskarīya, with the commentary of Parameśvara
697:
277:
Bhāskara I is considered the most important scholar of
1956:
1941:
Ramanujan Institute for Advanced Study in Mathematics
1686:
718:
650:
601:
564:
517:
394:
1037:
Department of mathematics, Lucknow University, 1960.
1023:. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
551:{\displaystyle {\frac {16}{5\pi }}-1\approx 1.859\%}
1076:S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (Hrsg.):
728:
685:
636:
576:
550:
500:
1142:
850:
743:He was the first mathematician to openly discuss
2076:
172:, and who gave a unique and remarkable rational
1030:. Madras Govt. Oriental series, no. cxxx, 1957.
1180:
973:. Birkäuser-Verlag Basel Stuttgart 1966 p. 90
767:, and the rising and setting of the planets.
156:) was a 7th-century Indian mathematician and
27:Indian mathematician and astronomer (600-680)
383:a remarkable approximation formula for sin x
288:
930:Nasa Space Science Data Coordinated Archive
1708:Kerala school of astronomy and mathematics
1187:
1173:
1080:. Verlag Harri Thun, Frankfurt a. M. 1990
262:in the eastern Punjab, which was ruled by
149:to avoid confusion with the 12th-century
1936:Homi Bhabha Centre for Science Education
958:Census of the Exact Sciences in Sanskrit
353:
219:, named in honour of the mathematician.
1154:MacTutor History of Mathematics Archive
1123:
1104:
1094:. John Wiley & Sons, New York 2000
1065:Springer-Verlag Berlin Heidelberg 2003
1012:
949:
912:
886:
788:Bhāskara I's sine approximation formula
591:. For instance, he posed the problem: "
124:Bhāskara I's sine approximation formula
14:
2077:
1194:
747:with four unequal, nonparallel sides.
1168:
712:, he criticized its approximation to
882:
880:
878:
876:
874:
846:
844:
842:
815:
813:
1461:Subbayya Sivasankaranarayana Pillai
250:region of the present-day state of
204:("Great Book of Bhāskara") and the
30:For others with the same name, see
24:
1921:Institute of Mathematical Sciences
1055:
851:O'Connor, J. J.; Robertson, E. F.
545:
213:Indian Space Research Organisation
25:
2131:
2085:7th-century Indian mathematicians
1931:Harish-Chandra Research Institute
1441:K. R. Parthasarathy (probabilist)
871:
839:
810:
2062:
2050:
2038:
2026:
2014:
2002:
1990:
1978:
1966:
1092:The Universal History of Numbers
1078:Lexikon bedeutender Mathematiker
346:in a scientific contribution in
696:Bhāskara clearly believed that
476:
334:, using a small circle for the
281:'s astronomical school. He and
2090:7th-century Indian astronomers
1916:Chennai Mathematical Institute
1285:Melpathur Narayana Bhattathiri
976:
963:
943:
918:
906:
887:Hayashi, Takao (1 July 2019).
704:was irrational. In support of
686:{\displaystyle y^{2}-8x^{2}=1}
637:{\displaystyle 8x^{2}+1=y^{2}}
495:
477:
467:
455:
428:
416:
369:, an astronomical treatise by
358:
180:function in his commentary on
13:
1:
803:
798:List of Indian mathematicians
254:in India. Also mentioned are
135:
77:
52:
1906:Indian Statistical Institute
952:, p. xiii) cites , and
750:
729:{\displaystyle {\sqrt {10}}}
222:
208:("Small Book of Bhāskara").
7:
2110:Scientists from Maharashtra
1926:Indian Institute of Science
1911:Bhaskaracharya Pratishthana
1789:A. A. Krishnaswamy Ayyangar
1754:Shankar Balakrishna Dikshit
1681:Hindu–Arabic numeral system
781:
774:were later translated into
235:education from his father.
166:Hindu–Arabic decimal system
160:who was the first to write
10:
2136:
1421:Subrahmanyan Chandrasekhar
1006:
736:, a practice common among
231:. Bhāskara I received his
184:'s work. This commentary,
29:
2115:Scholars from Maharashtra
1896:
1860:
1834:
1738:
1700:
1666:
1503:
1431:Veeravalli S. Varadarajan
1398:
1257:
1211:
1202:
317:. Similar to our current
295:positional numeral system
289:Representation of numbers
258:in southern Gujarat, and
119:
111:
103:
73:
48:
41:
32:Bhaskara (disambiguation)
1847:Henry Thomas Colebrooke
1436:S. R. Srinivasa Varadhan
1159:University of St Andrews
1124:Keller, Agathe (2006b),
1105:Keller, Agathe (2006a),
853:"Bhāskara I – Biography"
115:Mathematician, scientist
2100:Scientists from Gujarat
1320:Mādhava of Saṅgamagrāma
893:Encyclopedia Britannica
730:
687:
638:
578:
552:
502:
168:with a circle for the
2105:Scholars from Gujarat
1531:Brāhmasphuṭasiddhānta
731:
688:
639:
579:
553:
503:
354:Further contributions
1807:T. A. Saraswati Amma
1518:Bakhshali manuscript
1486:Kannan Soundararajan
1145:Robertson, Edmund F.
969:B. van der Waerden:
716:
708:'s approximation of
648:
599:
562:
515:
392:
242:(the capital of the
217:Bhāskara I satellite
211:On 7 June 1979, the
1883:Islamic mathematics
1842:Walter Eugene Clark
1636:Vasishtha Siddhanta
1608:Siddhānta Shiromani
1587:Paitamaha Siddhanta
1466:Tilak Raj Prabhakar
1411:Satyendra Nath Bose
1406:Srinivasa Ramanujan
1360:Nilakantha Somayaji
1143:O'Connor, John J.;
1063:4000 Jahre Algebra.
990:. 28 September 2020
960:, volume 4, p. 297.
793:List of astronomers
577:{\displaystyle x=0}
270:and later moved to
145:) (commonly called
2095:7th-century deaths
1375:Gangesha Upadhyaya
1196:Indian mathematics
726:
683:
634:
574:
548:
498:
1954:
1953:
1760:Sudhakara Dvivedi
1580:Paulisa Siddhanta
1499:
1498:
1355:Jagannatha Samrat
1350:Achyuta Pisharati
1015:, p. xiii))
740:mathematicians.
724:
531:
471:
186:Āryabhaṭīyabhāṣya
129:
128:
16:(Redirected from
2127:
2067:
2066:
2055:
2054:
2053:
2043:
2042:
2041:
2031:
2030:
2029:
2019:
2018:
2007:
2006:
2005:
1995:
1994:
1983:
1982:
1981:
1971:
1970:
1969:
1962:
1594:Romaka Siddhanta
1476:Akshay Venkatesh
1446:M. S. Narasimhan
1416:P.C. Mahalanobis
1209:
1208:
1189:
1182:
1175:
1166:
1165:
1161:
1138:
1119:
1000:
999:
997:
995:
980:
974:
967:
961:
947:
941:
940:
938:
936:
922:
916:
910:
904:
903:
901:
899:
884:
869:
868:
866:
864:
848:
837:
836:
834:
832:
825:Encyclopedia.com
817:
735:
733:
732:
727:
725:
720:
711:
701:
692:
690:
689:
684:
676:
675:
660:
659:
643:
641:
640:
635:
633:
632:
614:
613:
589:Pell's equations
583:
581:
580:
575:
557:
555:
554:
549:
532:
530:
519:
507:
505:
504:
499:
472:
470:
445:
444:
431:
408:
244:Maitraka dynasty
144:
140:
137:
82:
79:
57:
54:
39:
38:
21:
2135:
2134:
2130:
2129:
2128:
2126:
2125:
2124:
2075:
2074:
2073:
2061:
2051:
2049:
2039:
2037:
2027:
2025:
2013:
2003:
2001:
1989:
1979:
1977:
1967:
1965:
1957:
1955:
1950:
1898:
1892:
1856:
1830:
1801:C. T. Rajagopal
1748:Bapudeva Sastri
1740:
1734:
1696:
1676:Brahmi numerals
1668:
1662:
1622:Surya Siddhanta
1495:
1471:Manjul Bhargava
1394:
1253:
1198:
1193:
1136:
1117:
1058:
1056:Further reading
1009:
1004:
1003:
993:
991:
982:
981:
977:
968:
964:
948:
944:
934:
932:
924:
923:
919:
915:, p. xiii)
911:
907:
897:
895:
885:
872:
862:
860:
849:
840:
830:
828:
819:
818:
811:
806:
784:
753:
719:
717:
714:
713:
709:
699:
671:
667:
655:
651:
649:
646:
645:
628:
624:
609:
605:
600:
597:
596:
563:
560:
559:
523:
518:
516:
513:
512:
440:
436:
432:
409:
407:
393:
390:
389:
361:
356:
344:Brahmi numerals
332:Brahmi numerals
291:
225:
206:Laghubhāskarīya
142:
138:
99:
84:
80:
69:
59:
55:
44:
35:
28:
23:
22:
15:
12:
11:
5:
2133:
2123:
2122:
2117:
2112:
2107:
2102:
2097:
2092:
2087:
2072:
2071:
2059:
2047:
2035:
2023:
2011:
1999:
1987:
1975:
1952:
1951:
1949:
1948:
1943:
1938:
1933:
1928:
1923:
1918:
1913:
1908:
1902:
1900:
1894:
1893:
1891:
1890:
1885:
1880:
1875:
1870:
1864:
1862:
1858:
1857:
1855:
1854:
1849:
1844:
1838:
1836:
1832:
1831:
1829:
1828:
1822:
1816:
1810:
1804:
1798:
1792:
1786:
1781:
1775:
1772:P. C. Sengupta
1769:
1763:
1757:
1751:
1744:
1742:
1736:
1735:
1733:
1732:
1710:
1704:
1702:
1698:
1697:
1695:
1694:
1689:
1683:
1678:
1672:
1670:
1664:
1663:
1661:
1660:
1653:
1646:
1639:
1632:
1629:Tantrasamgraha
1625:
1618:
1611:
1604:
1597:
1590:
1583:
1576:
1569:
1562:
1555:
1552:Karanapaddhati
1548:
1541:
1538:Ganita Kaumudi
1534:
1527:
1520:
1515:
1507:
1505:
1501:
1500:
1497:
1496:
1494:
1493:
1488:
1483:
1478:
1473:
1468:
1463:
1458:
1456:Harish-Chandra
1453:
1451:C. S. Seshadri
1448:
1443:
1438:
1433:
1428:
1423:
1418:
1413:
1408:
1402:
1400:
1396:
1395:
1393:
1392:
1387:
1385:Sankara Variar
1382:
1377:
1372:
1367:
1362:
1357:
1352:
1347:
1342:
1337:
1332:
1327:
1322:
1317:
1312:
1307:
1302:
1297:
1292:
1287:
1282:
1277:
1272:
1267:
1261:
1259:
1255:
1254:
1252:
1251:
1246:
1241:
1236:
1231:
1226:
1221:
1215:
1213:
1206:
1204:Mathematicians
1200:
1199:
1192:
1191:
1184:
1177:
1169:
1163:
1162:
1140:
1134:
1121:
1115:
1102:
1088:
1074:
1057:
1054:
1053:
1052:
1047:K. S. Shukla.
1045:
1040:K. S. Shukla.
1038:
1033:K. S. Shukla.
1031:
1024:
1008:
1005:
1002:
1001:
975:
962:
942:
917:
905:
870:
838:
808:
807:
805:
802:
801:
800:
795:
790:
783:
780:
772:Mahābhāskarīya
757:Mahābhāskarīya
752:
749:
745:quadrilaterals
723:
682:
679:
674:
670:
666:
663:
658:
654:
631:
627:
623:
620:
617:
612:
608:
604:
573:
570:
567:
547:
544:
541:
538:
535:
529:
526:
522:
509:
508:
497:
494:
491:
488:
485:
482:
479:
475:
469:
466:
463:
460:
457:
454:
451:
448:
443:
439:
435:
430:
427:
424:
421:
418:
415:
412:
406:
403:
400:
397:
379:Mahābhāskarīya
360:
357:
355:
352:
290:
287:
224:
221:
202:Mahābhāskarīya
127:
126:
121:
120:Known for
117:
116:
113:
109:
108:
105:
101:
100:
85:
75:
71:
70:
60:
50:
46:
45:
42:
26:
9:
6:
4:
3:
2:
2132:
2121:
2118:
2116:
2113:
2111:
2108:
2106:
2103:
2101:
2098:
2096:
2093:
2091:
2088:
2086:
2083:
2082:
2080:
2070:
2065:
2060:
2058:
2048:
2046:
2036:
2034:
2024:
2022:
2017:
2012:
2010:
2000:
1998:
1993:
1988:
1986:
1976:
1974:
1964:
1963:
1960:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1903:
1901:
1895:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1869:
1866:
1865:
1863:
1861:Other regions
1859:
1853:
1852:David Pingree
1850:
1848:
1845:
1843:
1840:
1839:
1837:
1833:
1826:
1823:
1820:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1793:
1790:
1787:
1785:
1782:
1779:
1776:
1773:
1770:
1767:
1766:M. Rangacarya
1764:
1761:
1758:
1755:
1752:
1749:
1746:
1745:
1743:
1739:Historians of
1737:
1730:
1726:
1722:
1718:
1714:
1713:Jantar Mantar
1711:
1709:
1706:
1705:
1703:
1699:
1693:
1690:
1688:
1684:
1682:
1679:
1677:
1674:
1673:
1671:
1665:
1659:
1658:
1654:
1652:
1651:
1647:
1645:
1644:
1640:
1638:
1637:
1633:
1631:
1630:
1626:
1624:
1623:
1619:
1617:
1616:
1612:
1610:
1609:
1605:
1603:
1602:
1598:
1596:
1595:
1591:
1589:
1588:
1584:
1582:
1581:
1577:
1575:
1574:
1570:
1568:
1567:
1563:
1561:
1560:
1556:
1554:
1553:
1549:
1547:
1546:
1542:
1540:
1539:
1535:
1533:
1532:
1528:
1526:
1525:
1521:
1519:
1516:
1514:
1513:
1509:
1508:
1506:
1502:
1492:
1489:
1487:
1484:
1482:
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1422:
1419:
1417:
1414:
1412:
1409:
1407:
1404:
1403:
1401:
1397:
1391:
1388:
1386:
1383:
1381:
1378:
1376:
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1336:
1333:
1331:
1330:Mahendra Sūri
1328:
1326:
1323:
1321:
1318:
1316:
1313:
1311:
1308:
1306:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1266:
1263:
1262:
1260:
1256:
1250:
1247:
1245:
1242:
1240:
1237:
1235:
1232:
1230:
1227:
1225:
1222:
1220:
1217:
1216:
1214:
1210:
1207:
1205:
1201:
1197:
1190:
1185:
1183:
1178:
1176:
1171:
1170:
1167:
1160:
1156:
1155:
1150:
1146:
1141:
1137:
1135:3-7643-7292-3
1131:
1127:
1122:
1118:
1116:3-7643-7291-5
1112:
1108:
1103:
1101:
1100:0-471-39340-1
1097:
1093:
1089:
1087:
1086:3-8171-1164-9
1083:
1079:
1075:
1072:
1071:3-540-43554-9
1068:
1064:
1060:
1059:
1050:
1046:
1043:
1039:
1036:
1032:
1029:
1025:
1022:
1019:M. C. Apaṭe.
1018:
1017:
1016:
1014:
1013:Keller (2006a
989:
985:
979:
972:
966:
959:
955:
951:
950:Keller (2006a
946:
931:
927:
921:
914:
913:Keller (2006a
909:
894:
890:
883:
881:
879:
877:
875:
858:
857:Maths History
854:
847:
845:
843:
826:
822:
816:
814:
809:
799:
796:
794:
791:
789:
786:
785:
779:
777:
773:
768:
766:
762:
758:
748:
746:
741:
739:
721:
707:
703:
702:
694:
680:
677:
672:
668:
664:
661:
656:
652:
629:
625:
621:
618:
615:
610:
606:
602:
594:
590:
585:
571:
568:
565:
542:
539:
536:
533:
527:
524:
520:
492:
489:
486:
483:
480:
473:
464:
461:
458:
452:
449:
446:
441:
437:
433:
425:
422:
419:
413:
410:
404:
401:
398:
395:
388:
387:
386:
384:
380:
375:
372:
368:
367:
351:
349:
345:
341:
337:
333:
329:
323:
320:
316:
312:
308:
304:
300:
296:
286:
284:
280:
275:
273:
269:
265:
261:
257:
253:
249:
245:
241:
236:
234:
230:
220:
218:
215:launched the
214:
209:
207:
203:
199:
195:
191:
187:
183:
179:
175:
174:approximation
171:
167:
163:
159:
155:
152:
151:mathematician
148:
133:
125:
122:
118:
114:
112:Occupation(s)
110:
106:
102:
97:
93:
90:(present-day
89:
76:
72:
68:
64:
51:
47:
40:
37:
33:
19:
2057:Solar System
1899:institutions
1819:K. S. Shukla
1791:(1892– 1953)
1657:Yavanajataka
1655:
1648:
1641:
1634:
1627:
1620:
1615:Śulba Sūtras
1613:
1606:
1601:Sadratnamala
1599:
1592:
1585:
1578:
1571:
1564:
1557:
1550:
1545:Kanakkusaram
1543:
1536:
1529:
1522:
1510:
1380:Varāhamihira
1345:Parameshvara
1300:Govindasvāmi
1274:
1270:Āryabhaṭa II
1152:
1149:"Bhāskara I"
1125:
1106:
1091:
1077:
1062:
1048:
1041:
1034:
1027:
1020:
1010:
992:. Retrieved
987:
978:
970:
965:
957:
945:
935:16 September
933:. Retrieved
929:
920:
908:
896:. Retrieved
892:
889:"Bhāskara I"
861:. Retrieved
856:
829:. Retrieved
824:
821:"Bhāskara I"
771:
769:
761:conjunctions
756:
754:
742:
698:
695:
592:
586:
510:
378:
376:
364:
362:
327:
324:
314:
310:
306:
302:
298:
292:
276:
237:
233:astronomical
226:
210:
205:
201:
185:
146:
131:
130:
36:
2045:Outer space
2033:Spaceflight
1997:Mathematics
1835:Translators
1827:(1919–2005)
1825:K. V. Sarma
1821:(1918–2007)
1815:(1918–1992)
1809:(1918–2000)
1803:(1903–1978)
1797:(1901–1954)
1795:A. N. Singh
1780:(1888–1958)
1778:B. B. Datta
1774:(1876–1962)
1768:(1861–1916)
1762:(1855–1910)
1756:(1853–1898)
1750:(1821–1900)
1741:mathematics
1685:Symbol for
1669:innovations
1566:Lokavibhaga
1512:Aryabhatiya
1310:Jyeṣṭhadeva
1295:Brahmagupta
1280:Bhāskara II
1265:Āryabhaṭa I
1249:Yajnavalkya
994:3 September
898:12 December
831:12 December
366:Āryabhaṭīya
359:Mathematics
283:Brahmagupta
194:mathematics
154:Bhāskara II
104:Nationality
96:Maharashtra
2079:Categories
1784:T. Hayashi
1667:Pioneering
1650:Yuktibhāṣā
1573:Pātīgaṇita
1524:Bijaganita
1481:Ravi Vakil
1335:Munishvara
1315:Kamalakara
1290:Brahmadeva
1275:Bhāskara I
1224:Baudhayana
1090:G. Ifrah:
926:"Bhāskara"
804:References
328:ankair api
229:astronomer
158:astronomer
147:Bhāskara I
143: 680
141: – c.
139: 600
81: 680
56: 600
43:Bhāskara I
18:Bhaskara I
2009:Astronomy
1973:Biography
1813:S. N. Sen
1721:New Delhi
1643:Veṇvāroha
1504:Treatises
1305:Halayudha
1258:Classical
1229:Katyayana
1219:Apastamba
1026:v.harish
770:Parts of
751:Astronomy
706:Aryabhata
662:−
546:%
540:≈
534:−
528:π
493:π
490:≤
484:≤
462:−
459:π
447:−
438:π
423:−
420:π
405:≈
399:
377:His work
371:Aryabhata
279:Aryabhata
268:Saurastra
248:Saurastra
223:Biography
198:astronomy
182:Aryabhata
92:Telangana
86:possibly
63:Saurāṣṭra
61:possibly
2120:Acharyas
1729:Varanasi
1687:zero (0)
1559:Līlāvatī
1426:C.R. Rao
1390:Virasena
1370:Sridhara
1340:Narayana
1325:Mahāvīra
1073:, §3.2.1
782:See also
765:eclipses
348:Sanskrit
260:Thanesar
240:Vallabhi
190:Sanskrit
132:Bhāskara
2069:Science
1959:Portals
1868:Babylon
1701:Centres
1365:Śrīpati
1244:Pingala
1212:Ancient
1007:Sources
988:Cuemath
954:Pingree
340:decimal
319:decimal
256:Bharuch
252:Gujarat
176:of the
164:in the
162:numbers
1897:Modern
1888:Europe
1878:Greece
1725:Ujjain
1717:Jaipur
1399:Modern
1239:Pāṇini
1234:Manava
1132:
1113:
1098:
1084:
1069:
1011:(From
776:Arabic
315:senses
272:Aśmaka
264:Harsha
107:Indian
88:Aśmaka
67:Aśmaka
2021:Stars
1985:India
1873:China
863:5 May
543:1.859
309:, or
307:twins
303:wings
1946:TIFR
1130:ISBN
1111:ISBN
1096:ISBN
1082:ISBN
1067:ISBN
996:2022
937:2017
900:2022
865:2021
833:2022
755:The
738:Jain
644:(or
336:zero
311:eyes
299:moon
196:and
178:sine
170:zero
94:and
74:Died
49:Born
558:at
396:sin
192:on
65:or
2081::
1727:,
1723:,
1719:,
1157:,
1151:,
1147:,
986:.
956:,
928:.
891:.
873:^
855:.
841:^
823:.
812:^
778:.
722:10
521:16
411:16
385::
350:.
305:,
274:.
136:c.
83:CE
78:c.
58:CE
53:c.
1961::
1731:)
1715:(
1188:e
1181:t
1174:v
1139:.
1120:.
998:.
939:.
902:.
867:.
835:.
710:π
700:π
681:1
678:=
673:2
669:x
665:8
657:2
653:y
630:2
626:y
622:=
619:1
616:+
611:2
607:x
603:8
572:0
569:=
566:x
537:1
525:5
496:)
487:x
481:0
478:(
474:,
468:)
465:x
456:(
453:x
450:4
442:2
434:5
429:)
426:x
417:(
414:x
402:x
134:(
98:)
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.