1134:
791:
84:
contended, but he expressed them more clearly. His work is a highly syncopated approach to algebra and the emphasis in much of his text is on developing the techniques necessary to solve algebraic problems. He is highly respected among Indian mathematicians, because of his establishment of
679:
482:
1815:
1398:
289:
1129:{\displaystyle {\frac {1}{q}}={\frac {a_{1}}{q(q+a_{1})}}+{\frac {a_{2}}{(q+a_{1})(q+a_{1}+a_{2})}}+\dots +{\frac {a_{n-1}}{(q+a_{1}+\dots +a_{n-2})(q+a_{1}+\dots +a_{n-1})}}+{\frac {a_{n}}{a_{n}(q+a_{1}+\dots +a_{n-1})}}}
1604:
503:
340:
1693:
1285:
89:
for concepts such as equilateral, and isosceles triangle; rhombus; circle and semicircle. Mahāvīra's eminence spread throughout southern India and his books proved inspirational to other mathematicians in
330:
When the result is one, the denominators of the quantities having one as numerators are beginning with one and multiplied by three, in order. The first and the last are multiplied by two and two-thirds
776:
157:/ . He devised a formula which approximated the area and perimeters of ellipses and found methods to calculate the square of a number and cube roots of a number. He asserted that the
1461:
1218:
2947:
2912:
1884:
1638:
1507:
1168:
713:
1855:
1835:
1678:
1658:
1481:
1418:
3099:
1321:
207:
2649:
674:{\displaystyle 1={\frac {1}{2\cdot 3\cdot 1/2}}+{\frac {1}{3\cdot 4\cdot 1/2}}+\dots +{\frac {1}{(2n-1)\cdot 2n\cdot 1/2}}+{\frac {1}{2n\cdot 1/2}}}
1514:
2924:
477:{\displaystyle 1={\frac {1}{1\cdot 2}}+{\frac {1}{3}}+{\frac {1}{3^{2}}}+\dots +{\frac {1}{3^{n-2}}}+{\frac {1}{{\frac {2}{3}}\cdot 3^{n-1}}}}
1810:{\displaystyle {\frac {p}{q}}={\frac {a}{{\frac {ai+b}{p}}\cdot {\frac {q}{i}}}}+{\frac {b}{{\frac {ai+b}{p}}\cdot {\frac {q}{i}}\cdot {i}}}}
2345:
3079:
2971:
2128:
1229:
3125:
2866:
3041:
3094:
2218:
1300:
3104:
3046:
2281:
2261:
2241:
2184:
2150:
76:
from mathematics. It is the earliest Indian text entirely devoted to mathematics. He expounded on the same subjects on which
2619:
2141:
3130:
3089:
2599:
2081:
3135:
2338:
2290:
Kusuba, Takanori (2004), "Indian Rules for the
Decomposition of Fractions", in Charles Burnett; Jan P. Hogendijk;
2839:
1980:
The Math Book: From
Pythagoras to the 57th Dimension, 250 Milestones in the ... by Clifford A. Pickover: page 88
165:
does not exist. Arithmetic operations utilized in his works like Gaṇita-sāra-saṅgraha(Ganita Sara
Sangraha) uses
56:
3074:
2689:
2443:
2307:
17:
722:
2362:
1908:
1423:
3064:
3145:
3084:
3069:
2331:
2253:
Groundbreaking
Scientific Experiments, Inventions, and Discoveries of the Middle Ages and the Renaissance
2579:
1186:
2589:
2879:
2745:
2594:
2223:
2213:
3005:
2887:
2478:
3026:
2953:
2166:
2766:
2271:
2251:
2883:
2875:
2377:
2231:
2197:
2965:
2676:
2644:
2172:
2157:(Available, along with many other entries from other encyclopaedias for other Mahāvīra-s,
1860:
8:
3031:
3000:
2808:
2794:
2731:
2624:
2569:
2564:
2518:
2468:
2209:
2168:
Encyclopaedia of the
History of Science, Technology, and Medicine in Non-Western Cultures
1615:
1486:
1145:
690:
166:
2176:
2067:
A Concise
History of Science in India (Eds.) D. M. Bose, S. N. Sen and B.V. Subbarayappa
2533:
2354:
2075:
1840:
1820:
1663:
1643:
1466:
1403:
1393:{\displaystyle {\frac {1}{n}}={\frac {1}{p\cdot n}}+{\frac {1}{\frac {p\cdot n}{n-1}}}}
284:{\displaystyle 1+{\tfrac {1}{3}}+{\tfrac {1}{3\cdot 4}}-{\tfrac {1}{3\cdot 4\cdot 34}}}
190:
2158:
2065:
3140:
3036:
2918:
2738:
2513:
2508:
2382:
2313:
2303:
2277:
2257:
2237:
2180:
2146:
186:
2752:
2634:
2604:
2574:
2299:
99:
64:) or the Compendium on the gist of Mathematics in 850 CE. He was patronised by the
2717:
2488:
173:. However, he erroneously states that a number divided by zero remains unchanged.
2959:
2906:
2834:
2780:
2629:
2498:
1896:
162:
95:
2538:
2458:
2930:
2850:
2787:
2710:
2696:
2614:
2609:
2543:
2387:
91:
2438:
3119:
3010:
2942:
2871:
2773:
2317:
2193:
2136:
1599:{\displaystyle {\frac {1}{a\cdot b}}={\frac {1}{a(a+b)}}+{\frac {1}{b(a+b)}}}
194:
43:
2433:
2397:
2977:
2815:
2759:
2703:
2523:
2503:
2428:
69:
2983:
2936:
2724:
2670:
2453:
2407:
2291:
1998:
Geometry in
Ancient and Medieval India by T. A. Sarasvati Amma: page 122
158:
86:
81:
65:
1989:
Algebra: Sets, Symbols, and the
Language of Thought by John Tabak: p.43
2682:
2639:
2493:
2473:
2448:
2296:
Studies in the
History of the Exact Sciences in Honour of David Pingree
1308:
To express a unit fraction as the sum of two other unit fractions (GSS
1291:
and repeat the process for the second term, recursively. (Note that if
2801:
2463:
2423:
2323:
77:
2019:
Census of the Exact
Sciences in Sanskrit by David Pingree: page 388
2584:
2548:
2528:
1280:{\displaystyle {\frac {p}{q}}={\frac {1}{r}}+{\frac {i}{r\cdot q}}}
302:(lit. "the operation of the reduction of fractions"). In this, the
73:
2402:
2650:
Shanti Swarup Bhatnagar Prize recipients in Mathematical Science
2070:. Indian National Science Academy. 15 October 1971. p. 167.
1932:
490:
To express 1 as the sum of an odd number of unit fractions (GSS
298:(GSS), the second section of the chapter on arithmetic is named
2392:
47:
2273:
Mathematical Achievements of Pre-modern Indian Mathematicians
51:
1964:
1962:
40:
2851:
Infinite series expansions for the trigonometric functions
1959:
1640:
as the sum of two other fractions with given numerators
2126:
Bibhutibhusan Datta and Avadhesh Narayan Singh (1962).
185:
gave systematic rules for expressing a fraction as the
1191:
306:
section (verses 55–98) gives rules for the following:
256:
233:
218:
3100:
Ramanujan Institute for Advanced Study in Mathematics
2845:
2207:
2046:
1949:
1947:
1938:
1863:
1843:
1823:
1696:
1666:
1646:
1618:
1517:
1489:
1469:
1426:
1406:
1324:
1232:
1189:
1148:
794:
725:
693:
506:
343:
210:
170:
2034:
323:
rūpāṃśakarāśīnāṃ rūpādyās triguṇitā harāḥ kramaśaḥ /
2233:
Algebra: Sets, Symbols, and the Language of Thought
2022:
39:, "Mahavira the Teacher") was a 9th-century Indian
2001:
1944:
1920:
1878:
1849:
1829:
1809:
1672:
1652:
1632:
1598:
1501:
1475:
1455:
1412:
1392:
1279:
1212:
1162:
1128:
770:
707:
673:
476:
283:
176:
3117:
325:dvidvitryaṃśābhyastāv ādimacaramau phale rūpe //
2339:
189:. This follows the use of unit fractions in
2129:History of Hindu Mathematics: A Source Book
2867:Kerala school of astronomy and mathematics
2346:
2332:
2269:
1968:
3095:Homi Bhabha Centre for Science Education
771:{\displaystyle a_{1},a_{2},\dots ,a_{n}}
109:He discovered algebraic identities like
2219:MacTutor History of Mathematics Archive
2192:
2135:
2107:
2105:
2103:
2101:
2099:
2097:
2095:
2093:
2091:
2007:
1926:
1456:{\displaystyle {\frac {p\cdot n}{n-1}}}
1301:greedy algorithm for Egyptian fractions
1299:such integer, this is identical to the
14:
3118:
2353:
2289:
2111:
719:other fractions with given numerators
2327:
2249:
2229:
2164:
2145:. New York: Charles Scribner's Sons.
2052:
2040:
2028:
1953:
1891:Some further rules were given in the
149:. He also found out the formula for C
2088:
2620:Subbayya Sivasankaranarayana Pillai
24:
3080:Institute of Mathematical Sciences
2142:Dictionary of Scientific Biography
25:
3157:
3126:9th-century Indian mathematicians
3090:Harish-Chandra Research Institute
2600:K. R. Parthasarathy (probabilist)
1213:{\displaystyle {\tfrac {q+i}{p}}}
1170:as a sum of unit fractions (GSS
27:9th-century Indian mathematician
2058:
177:Rules for decomposing fractions
3075:Chennai Mathematical Institute
2444:Melpathur Narayana Bhattathiri
2256:, Greenwood Publishing Group,
2013:
1992:
1983:
1974:
1590:
1578:
1560:
1548:
1120:
1076:
1044:
1000:
997:
953:
919:
887:
884:
865:
843:
824:
610:
595:
13:
1:
2120:
2080:: CS1 maint: date and year (
1939:O'Connor & Robertson 2000
1909:List of Indian mathematicians
197:' giving an approximation of
193:in the Vedic period, and the
94:. It was translated into the
3065:Indian Statistical Institute
7:
3085:Indian Institute of Science
3070:Bhaskaracharya Pratishthana
2948:A. A. Krishnaswamy Ayyangar
2913:Shankar Balakrishna Dikshit
2840:Hindu–Arabic numeral system
1902:
1295:is always chosen to be the
687:To express a unit fraction
310:To express 1 as the sum of
10:
3162:
2580:Subrahmanyan Chandrasekhar
1837:is to be chosen such that
1420:is to be chosen such that
167:decimal place-value system
3055:
3019:
2993:
2897:
2859:
2825:
2662:
2590:Veeravalli S. Varadarajan
2557:
2416:
2370:
2361:
2250:Krebs, Robert E. (2004),
1463:is an integer (for which
3131:9th-century Indian Jains
3006:Henry Thomas Colebrooke
2595:S. R. Srinivasa Varadhan
2270:Puttaswamy, T.K (2012),
2224:University of St Andrews
1914:
1142:To express any fraction
3136:Scholars from Karnataka
2479:Mādhava of Saṅgamagrāma
2236:, Infobase Publishing,
2202:Encyclopædia Britannica
2165:Selin, Helaine (2008),
169:and include the use of
104:Saara Sangraha Ganitamu
2294:; et al. (eds.),
1880:
1851:
1831:
1811:
1674:
1654:
1634:
1612:To express a fraction
1600:
1503:
1483:must be a multiple of
1477:
1457:
1414:
1394:
1281:
1214:
1164:
1130:
772:
709:
675:
478:
333:
327:
300:kalā-savarṇa-vyavahāra
285:
2690:Brāhmasphuṭasiddhānta
1899:in the 14th century.
1881:
1852:
1832:
1812:
1675:
1655:
1635:
1601:
1504:
1478:
1458:
1415:
1395:
1282:
1215:
1165:
1131:
773:
710:
676:
479:
328:
321:
286:
187:sum of unit fractions
2966:T. A. Saraswati Amma
2677:Bakhshali manuscript
2645:Kannan Soundararajan
2230:Tabak, John (2009),
2210:Robertson, Edmund F.
2139:(1970). "Mahāvīra".
1879:{\displaystyle ai+b}
1861:
1841:
1821:
1694:
1664:
1644:
1616:
1515:
1487:
1467:
1424:
1404:
1322:
1230:
1187:
1174:80, examples in 81):
1146:
792:
782:78, examples in 79):
723:
691:
504:
341:
318:75, examples in 76):
314:unit fractions (GSS
296:Gaṇita-sāra-saṅgraha
208:
183:Gaṇita-sāra-saṅgraha
62:Ganita Sara Sangraha
57:Gaṇita-sāra-saṅgraha
3042:Islamic mathematics
3001:Walter Eugene Clark
2795:Vasishtha Siddhanta
2767:Siddhānta Shiromani
2746:Paitamaha Siddhanta
2625:Tilak Raj Prabhakar
2570:Satyendra Nath Bose
2565:Srinivasa Ramanujan
2519:Nilakantha Somayaji
2208:O'Connor, John J.;
2177:2008ehst.book.....S
1684:87, example in 88):
1633:{\displaystyle p/q}
1502:{\displaystyle n-1}
1312:85, example in 86):
1163:{\displaystyle p/q}
708:{\displaystyle 1/q}
3146:Rashtrakuta people
2534:Gangesha Upadhyaya
2355:Indian mathematics
2114:, pp. 497–516
1876:
1847:
1827:
1807:
1670:
1650:
1630:
1596:
1499:
1473:
1453:
1410:
1390:
1277:
1210:
1208:
1179:Choose an integer
1160:
1126:
768:
705:
671:
474:
281:
279:
250:
227:
191:Indian mathematics
3113:
3112:
2919:Sudhakara Dvivedi
2739:Paulisa Siddhanta
2658:
2657:
2514:Jagannatha Samrat
2509:Achyuta Pisharati
2283:978-0-12-397938-4
2263:978-0-313-32433-8
2243:978-0-8160-6875-3
2186:978-1-4020-4559-2
2152:978-0-684-10114-9
1850:{\displaystyle p}
1830:{\displaystyle i}
1805:
1794:
1781:
1751:
1748:
1735:
1705:
1673:{\displaystyle b}
1653:{\displaystyle a}
1594:
1564:
1534:
1476:{\displaystyle p}
1451:
1413:{\displaystyle p}
1388:
1387:
1354:
1333:
1275:
1254:
1241:
1207:
1124:
1048:
923:
847:
803:
669:
637:
578:
543:
472:
450:
431:
399:
379:
366:
278:
249:
226:
46:possibly born in
16:(Redirected from
3153:
2753:Romaka Siddhanta
2635:Akshay Venkatesh
2605:M. S. Narasimhan
2575:P.C. Mahalanobis
2368:
2367:
2348:
2341:
2334:
2325:
2324:
2320:
2286:
2266:
2246:
2226:
2204:
2189:
2156:
2115:
2109:
2086:
2085:
2079:
2071:
2062:
2056:
2050:
2044:
2038:
2032:
2026:
2020:
2017:
2011:
2005:
1999:
1996:
1990:
1987:
1981:
1978:
1972:
1966:
1957:
1951:
1942:
1936:
1930:
1924:
1885:
1883:
1882:
1877:
1856:
1854:
1853:
1848:
1836:
1834:
1833:
1828:
1816:
1814:
1813:
1808:
1806:
1804:
1803:
1795:
1787:
1782:
1777:
1763:
1757:
1752:
1750:
1749:
1741:
1736:
1731:
1717:
1711:
1706:
1698:
1679:
1677:
1676:
1671:
1659:
1657:
1656:
1651:
1639:
1637:
1636:
1631:
1626:
1605:
1603:
1602:
1597:
1595:
1593:
1570:
1565:
1563:
1540:
1535:
1533:
1519:
1508:
1506:
1505:
1500:
1482:
1480:
1479:
1474:
1462:
1460:
1459:
1454:
1452:
1450:
1439:
1428:
1419:
1417:
1416:
1411:
1399:
1397:
1396:
1391:
1389:
1386:
1375:
1364:
1360:
1355:
1353:
1339:
1334:
1326:
1286:
1284:
1283:
1278:
1276:
1274:
1260:
1255:
1247:
1242:
1234:
1219:
1217:
1216:
1211:
1209:
1203:
1192:
1169:
1167:
1166:
1161:
1156:
1135:
1133:
1132:
1127:
1125:
1123:
1119:
1118:
1094:
1093:
1075:
1074:
1064:
1063:
1054:
1049:
1047:
1043:
1042:
1018:
1017:
996:
995:
971:
970:
951:
950:
935:
924:
922:
918:
917:
905:
904:
883:
882:
863:
862:
853:
848:
846:
842:
841:
819:
818:
809:
804:
796:
777:
775:
774:
769:
767:
766:
748:
747:
735:
734:
714:
712:
711:
706:
701:
680:
678:
677:
672:
670:
668:
664:
643:
638:
636:
632:
590:
579:
577:
573:
549:
544:
542:
538:
514:
483:
481:
480:
475:
473:
471:
470:
469:
451:
443:
437:
432:
430:
429:
411:
400:
398:
397:
385:
380:
372:
367:
365:
351:
290:
288:
287:
282:
280:
277:
257:
251:
248:
234:
228:
219:
203:
202:
100:Pavuluri Mallana
21:
3161:
3160:
3156:
3155:
3154:
3152:
3151:
3150:
3116:
3115:
3114:
3109:
3057:
3051:
3015:
2989:
2960:C. T. Rajagopal
2907:Bapudeva Sastri
2899:
2893:
2855:
2835:Brahmi numerals
2827:
2821:
2781:Surya Siddhanta
2654:
2630:Manjul Bhargava
2553:
2412:
2357:
2352:
2310:
2284:
2264:
2244:
2187:
2153:
2123:
2118:
2110:
2089:
2073:
2072:
2064:
2063:
2059:
2055:, p. 1268.
2051:
2047:
2039:
2035:
2027:
2023:
2018:
2014:
2006:
2002:
1997:
1993:
1988:
1984:
1979:
1975:
1969:Puttaswamy 2012
1967:
1960:
1952:
1945:
1937:
1933:
1925:
1921:
1917:
1905:
1862:
1859:
1858:
1842:
1839:
1838:
1822:
1819:
1818:
1799:
1786:
1764:
1762:
1761:
1756:
1740:
1718:
1716:
1715:
1710:
1697:
1695:
1692:
1691:
1665:
1662:
1661:
1645:
1642:
1641:
1622:
1617:
1614:
1613:
1574:
1569:
1544:
1539:
1523:
1518:
1516:
1513:
1512:
1488:
1485:
1484:
1468:
1465:
1464:
1440:
1429:
1427:
1425:
1422:
1421:
1405:
1402:
1401:
1376:
1365:
1359:
1343:
1338:
1325:
1323:
1320:
1319:
1264:
1259:
1246:
1233:
1231:
1228:
1227:
1193:
1190:
1188:
1185:
1184:
1152:
1147:
1144:
1143:
1108:
1104:
1089:
1085:
1070:
1066:
1065:
1059:
1055:
1053:
1032:
1028:
1013:
1009:
985:
981:
966:
962:
952:
940:
936:
934:
913:
909:
900:
896:
878:
874:
864:
858:
854:
852:
837:
833:
820:
814:
810:
808:
795:
793:
790:
789:
762:
758:
743:
739:
730:
726:
724:
721:
720:
697:
692:
689:
688:
660:
647:
642:
628:
594:
589:
569:
553:
548:
534:
518:
513:
505:
502:
501:
459:
455:
442:
441:
436:
419:
415:
410:
393:
389:
384:
371:
355:
350:
342:
339:
338:
324:
261:
255:
238:
232:
217:
209:
206:
205:
200:
198:
179:
163:negative number
156:
154:
96:Telugu language
72:. He separated
28:
23:
22:
15:
12:
11:
5:
3159:
3149:
3148:
3143:
3138:
3133:
3128:
3111:
3110:
3108:
3107:
3102:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3061:
3059:
3053:
3052:
3050:
3049:
3044:
3039:
3034:
3029:
3023:
3021:
3017:
3016:
3014:
3013:
3008:
3003:
2997:
2995:
2991:
2990:
2988:
2987:
2981:
2975:
2969:
2963:
2957:
2951:
2945:
2940:
2934:
2931:P. C. Sengupta
2928:
2922:
2916:
2910:
2903:
2901:
2895:
2894:
2892:
2891:
2869:
2863:
2861:
2857:
2856:
2854:
2853:
2848:
2842:
2837:
2831:
2829:
2823:
2822:
2820:
2819:
2812:
2805:
2798:
2791:
2788:Tantrasamgraha
2784:
2777:
2770:
2763:
2756:
2749:
2742:
2735:
2728:
2721:
2714:
2711:Karanapaddhati
2707:
2700:
2697:Ganita Kaumudi
2693:
2686:
2679:
2674:
2666:
2664:
2660:
2659:
2656:
2655:
2653:
2652:
2647:
2642:
2637:
2632:
2627:
2622:
2617:
2615:Harish-Chandra
2612:
2610:C. S. Seshadri
2607:
2602:
2597:
2592:
2587:
2582:
2577:
2572:
2567:
2561:
2559:
2555:
2554:
2552:
2551:
2546:
2544:Sankara Variar
2541:
2536:
2531:
2526:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2471:
2466:
2461:
2456:
2451:
2446:
2441:
2436:
2431:
2426:
2420:
2418:
2414:
2413:
2411:
2410:
2405:
2400:
2395:
2390:
2385:
2380:
2374:
2372:
2365:
2363:Mathematicians
2359:
2358:
2351:
2350:
2343:
2336:
2328:
2322:
2321:
2308:
2287:
2282:
2267:
2262:
2247:
2242:
2227:
2205:
2194:Hayashi, Takao
2190:
2185:
2162:
2151:
2137:Pingree, David
2133:
2122:
2119:
2117:
2116:
2087:
2057:
2045:
2043:, p. 132.
2033:
2021:
2012:
2000:
1991:
1982:
1973:
1971:, p. 231.
1958:
1943:
1931:
1918:
1916:
1913:
1912:
1911:
1904:
1901:
1893:Gaṇita-kaumudi
1889:
1888:
1887:
1886:
1875:
1872:
1869:
1866:
1846:
1826:
1802:
1798:
1793:
1790:
1785:
1780:
1776:
1773:
1770:
1767:
1760:
1755:
1747:
1744:
1739:
1734:
1730:
1727:
1724:
1721:
1714:
1709:
1704:
1701:
1686:
1685:
1669:
1649:
1629:
1625:
1621:
1609:
1608:
1607:
1606:
1592:
1589:
1586:
1583:
1580:
1577:
1573:
1568:
1562:
1559:
1556:
1553:
1550:
1547:
1543:
1538:
1532:
1529:
1526:
1522:
1510:
1498:
1495:
1492:
1472:
1449:
1446:
1443:
1438:
1435:
1432:
1409:
1385:
1382:
1379:
1374:
1371:
1368:
1363:
1358:
1352:
1349:
1346:
1342:
1337:
1332:
1329:
1314:
1313:
1305:
1304:
1289:
1288:
1287:
1273:
1270:
1267:
1263:
1258:
1253:
1250:
1245:
1240:
1237:
1220:is an integer
1206:
1202:
1199:
1196:
1176:
1175:
1159:
1155:
1151:
1139:
1138:
1137:
1136:
1122:
1117:
1114:
1111:
1107:
1103:
1100:
1097:
1092:
1088:
1084:
1081:
1078:
1073:
1069:
1062:
1058:
1052:
1046:
1041:
1038:
1035:
1031:
1027:
1024:
1021:
1016:
1012:
1008:
1005:
1002:
999:
994:
991:
988:
984:
980:
977:
974:
969:
965:
961:
958:
955:
949:
946:
943:
939:
933:
930:
927:
921:
916:
912:
908:
903:
899:
895:
892:
889:
886:
881:
877:
873:
870:
867:
861:
857:
851:
845:
840:
836:
832:
829:
826:
823:
817:
813:
807:
802:
799:
784:
783:
765:
761:
757:
754:
751:
746:
742:
738:
733:
729:
715:as the sum of
704:
700:
696:
684:
683:
682:
681:
667:
663:
659:
656:
653:
650:
646:
641:
635:
631:
627:
624:
621:
618:
615:
612:
609:
606:
603:
600:
597:
593:
588:
585:
582:
576:
572:
568:
565:
562:
559:
556:
552:
547:
541:
537:
533:
530:
527:
524:
521:
517:
512:
509:
496:
495:
487:
486:
485:
484:
468:
465:
462:
458:
454:
449:
446:
440:
435:
428:
425:
422:
418:
414:
409:
406:
403:
396:
392:
388:
383:
378:
375:
370:
364:
361:
358:
354:
349:
346:
320:
319:
276:
273:
270:
267:
264:
260:
254:
247:
244:
241:
237:
231:
225:
222:
216:
213:
204:equivalent to
178:
175:
150:
92:Southern India
54:. He authored
37:Mahaviracharya
26:
18:Mahaviracharya
9:
6:
4:
3:
2:
3158:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3124:
3123:
3121:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3062:
3060:
3054:
3048:
3045:
3043:
3040:
3038:
3035:
3033:
3030:
3028:
3025:
3024:
3022:
3020:Other regions
3018:
3012:
3011:David Pingree
3009:
3007:
3004:
3002:
2999:
2998:
2996:
2992:
2985:
2982:
2979:
2976:
2973:
2970:
2967:
2964:
2961:
2958:
2955:
2952:
2949:
2946:
2944:
2941:
2938:
2935:
2932:
2929:
2926:
2925:M. Rangacarya
2923:
2920:
2917:
2914:
2911:
2908:
2905:
2904:
2902:
2898:Historians of
2896:
2889:
2885:
2881:
2877:
2873:
2872:Jantar Mantar
2870:
2868:
2865:
2864:
2862:
2858:
2852:
2849:
2847:
2843:
2841:
2838:
2836:
2833:
2832:
2830:
2824:
2818:
2817:
2813:
2811:
2810:
2806:
2804:
2803:
2799:
2797:
2796:
2792:
2790:
2789:
2785:
2783:
2782:
2778:
2776:
2775:
2771:
2769:
2768:
2764:
2762:
2761:
2757:
2755:
2754:
2750:
2748:
2747:
2743:
2741:
2740:
2736:
2734:
2733:
2729:
2727:
2726:
2722:
2720:
2719:
2715:
2713:
2712:
2708:
2706:
2705:
2701:
2699:
2698:
2694:
2692:
2691:
2687:
2685:
2684:
2680:
2678:
2675:
2673:
2672:
2668:
2667:
2665:
2661:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2576:
2573:
2571:
2568:
2566:
2563:
2562:
2560:
2556:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2530:
2527:
2525:
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2489:Mahendra Sūri
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2460:
2457:
2455:
2452:
2450:
2447:
2445:
2442:
2440:
2437:
2435:
2432:
2430:
2427:
2425:
2422:
2421:
2419:
2415:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2384:
2381:
2379:
2376:
2375:
2373:
2369:
2366:
2364:
2360:
2356:
2349:
2344:
2342:
2337:
2335:
2330:
2329:
2326:
2319:
2315:
2311:
2305:
2301:
2297:
2293:
2288:
2285:
2279:
2275:
2274:
2268:
2265:
2259:
2255:
2254:
2248:
2245:
2239:
2235:
2234:
2228:
2225:
2221:
2220:
2215:
2211:
2206:
2203:
2199:
2195:
2191:
2188:
2182:
2178:
2174:
2170:
2169:
2163:
2160:
2154:
2148:
2144:
2143:
2138:
2134:
2131:
2130:
2125:
2124:
2113:
2108:
2106:
2104:
2102:
2100:
2098:
2096:
2094:
2092:
2083:
2077:
2069:
2068:
2061:
2054:
2049:
2042:
2037:
2031:, p. 43.
2030:
2025:
2016:
2009:
2004:
1995:
1986:
1977:
1970:
1965:
1963:
1956:, p. 42.
1955:
1950:
1948:
1940:
1935:
1928:
1923:
1919:
1910:
1907:
1906:
1900:
1898:
1894:
1873:
1870:
1867:
1864:
1844:
1824:
1800:
1796:
1791:
1788:
1783:
1778:
1774:
1771:
1768:
1765:
1758:
1753:
1745:
1742:
1737:
1732:
1728:
1725:
1722:
1719:
1712:
1707:
1702:
1699:
1690:
1689:
1688:
1687:
1683:
1667:
1647:
1627:
1623:
1619:
1611:
1610:
1587:
1584:
1581:
1575:
1571:
1566:
1557:
1554:
1551:
1545:
1541:
1536:
1530:
1527:
1524:
1520:
1511:
1496:
1493:
1490:
1470:
1447:
1444:
1441:
1436:
1433:
1430:
1407:
1383:
1380:
1377:
1372:
1369:
1366:
1361:
1356:
1350:
1347:
1344:
1340:
1335:
1330:
1327:
1318:
1317:
1316:
1315:
1311:
1307:
1306:
1302:
1298:
1294:
1290:
1271:
1268:
1265:
1261:
1256:
1251:
1248:
1243:
1238:
1235:
1226:
1225:
1224:, then write
1223:
1204:
1200:
1197:
1194:
1182:
1178:
1177:
1173:
1157:
1153:
1149:
1141:
1140:
1115:
1112:
1109:
1105:
1101:
1098:
1095:
1090:
1086:
1082:
1079:
1071:
1067:
1060:
1056:
1050:
1039:
1036:
1033:
1029:
1025:
1022:
1019:
1014:
1010:
1006:
1003:
992:
989:
986:
982:
978:
975:
972:
967:
963:
959:
956:
947:
944:
941:
937:
931:
928:
925:
914:
910:
906:
901:
897:
893:
890:
879:
875:
871:
868:
859:
855:
849:
838:
834:
830:
827:
821:
815:
811:
805:
800:
797:
788:
787:
786:
785:
781:
763:
759:
755:
752:
749:
744:
740:
736:
731:
727:
718:
702:
698:
694:
686:
685:
665:
661:
657:
654:
651:
648:
644:
639:
633:
629:
625:
622:
619:
616:
613:
607:
604:
601:
598:
591:
586:
583:
580:
574:
570:
566:
563:
560:
557:
554:
550:
545:
539:
535:
531:
528:
525:
522:
519:
515:
510:
507:
500:
499:
498:
497:
493:
489:
488:
466:
463:
460:
456:
452:
447:
444:
438:
433:
426:
423:
420:
416:
412:
407:
404:
401:
394:
390:
386:
381:
376:
373:
368:
362:
359:
356:
352:
347:
344:
337:
336:
335:
334:
332:
326:
317:
313:
309:
308:
307:
305:
301:
297:
292:
274:
271:
268:
265:
262:
258:
252:
245:
242:
239:
235:
229:
223:
220:
214:
211:
196:
192:
188:
184:
174:
172:
168:
164:
160:
153:
148:
144:
140:
136:
132:
128:
124:
120:
116:
112:
107:
105:
101:
97:
93:
88:
83:
79:
75:
71:
67:
63:
59:
58:
53:
49:
45:
44:mathematician
42:
38:
34:
30:
19:
3058:institutions
2978:K. S. Shukla
2950:(1892– 1953)
2816:Yavanajataka
2814:
2807:
2800:
2793:
2786:
2779:
2774:Śulba Sūtras
2772:
2765:
2760:Sadratnamala
2758:
2751:
2744:
2737:
2730:
2723:
2716:
2709:
2704:Kanakkusaram
2702:
2695:
2688:
2681:
2669:
2539:Varāhamihira
2504:Parameshvara
2483:
2459:Govindasvāmi
2429:Āryabhaṭa II
2295:
2272:
2252:
2232:
2217:
2201:
2171:, Springer,
2167:
2140:
2127:
2066:
2060:
2048:
2036:
2024:
2015:
2008:Hayashi 2013
2003:
1994:
1985:
1976:
1934:
1927:Pingree 1970
1922:
1892:
1890:
1681:
1309:
1296:
1292:
1221:
1180:
1171:
779:
716:
491:
329:
322:
315:
311:
303:
299:
295:
293:
195:Śulba Sūtras
182:
180:
151:
146:
142:
138:
134:
130:
126:
122:
118:
114:
110:
108:
103:
70:Amoghavarsha
61:
55:
36:
32:
31:
29:
2994:Translators
2986:(1919–2005)
2984:K. V. Sarma
2980:(1918–2007)
2974:(1918–1992)
2968:(1918–2000)
2962:(1903–1978)
2956:(1901–1954)
2954:A. N. Singh
2939:(1888–1958)
2937:B. B. Datta
2933:(1876–1962)
2927:(1861–1916)
2921:(1855–1910)
2915:(1853–1898)
2909:(1821–1900)
2900:mathematics
2844:Symbol for
2828:innovations
2725:Lokavibhaga
2671:Aryabhatiya
2469:Jyeṣṭhadeva
2454:Brahmagupta
2439:Bhāskara II
2424:Āryabhaṭa I
2408:Yajnavalkya
2292:Kim Plofker
2112:Kusuba 2004
1682:kalāsavarṇa
1310:kalāsavarṇa
1172:kalāsavarṇa
780:kalāsavarṇa
492:kalāsavarṇa
316:kalāsavarṇa
181:Mahāvīra's
159:square root
87:terminology
82:Brahmagupta
66:Rashtrakuta
3120:Categories
2943:T. Hayashi
2826:Pioneering
2809:Yuktibhāṣā
2732:Pātīgaṇita
2683:Bijaganita
2640:Ravi Vakil
2494:Munishvara
2474:Kamalakara
2449:Brahmadeva
2434:Bhāskara I
2383:Baudhayana
2309:9004132023
2276:, Newnes,
2214:"Mahavira"
2198:"Mahavira"
2121:References
2053:Selin 2008
2041:Krebs 2004
2029:Tabak 2009
1954:Tabak 2009
1183:such that
2972:S. N. Sen
2880:New Delhi
2802:Veṇvāroha
2663:Treatises
2464:Halayudha
2417:Classical
2388:Katyayana
2378:Apastamba
2318:0169-8729
2076:cite book
1797:⋅
1784:⋅
1738:⋅
1528:⋅
1494:−
1445:−
1434:⋅
1381:−
1370:⋅
1348:⋅
1269:⋅
1113:−
1099:⋯
1037:−
1023:⋯
990:−
976:⋯
945:−
929:⋯
753:…
655:⋅
623:⋅
614:⋅
605:−
584:⋯
564:⋅
558:⋅
529:⋅
523:⋅
464:−
453:⋅
424:−
405:⋯
360:⋅
304:bhāgajāti
272:⋅
266:⋅
253:−
243:⋅
78:Aryabhata
74:astrology
3141:Acharyas
2888:Varanasi
2846:zero (0)
2718:Līlāvatī
2585:C.R. Rao
2549:Virasena
2529:Sridhara
2499:Narayana
2484:Mahāvīra
2212:(2000),
2196:(2013),
1903:See also
1897:Nārāyaṇa
1857:divides
1297:smallest
141:−
129:−
68:emperor
33:Mahāvīra
3027:Babylon
2860:Centres
2524:Śrīpati
2403:Pingala
2371:Ancient
2173:Bibcode
294:In the
199:√
3056:Modern
3047:Europe
3037:Greece
2884:Ujjain
2876:Jaipur
2558:Modern
2398:Pāṇini
2393:Manava
2316:
2306:
2280:
2260:
2240:
2183:
2159:online
2149:
1817:where
1400:where
48:Mysore
3032:China
2300:Brill
1915:Notes
1680:(GSS
778:(GSS
161:of a
52:India
50:, in
3105:TIFR
2314:ISSN
2304:ISBN
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