297:
42:
4886:
2757:
313:
372:
Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The
Treatise on the Chord and Sine”, when he died, in 1429. Some state that he was murdered and say that Ulugh Beg probably ordered this, whereas others suggest he died a natural death. Regardless, after his death,
350:, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world's greatest mathematicians.
935:
180 years later. Al-Kashi's goal was to compute the circle constant so precisely that the circumference of the largest possible circle (ecliptica) could be computed with the highest desirable precision (the diameter of a hair).
1785:
41:
1648:
1881:
854:
4905:
1839:
1810:
1705:
1680:
1547:
2056:
761:
296:
4894:
1073:
365:
and beyond, flocked to this academy in the capital city of Ulugh Beg's empire. Consequently, Ulugh Beg gathered many great mathematicians and scientists of the
4940:
4309:
2894:
2252:
Kennedy, Edward S. (1952), "A Fifteenth-Century
Planetary Computer: al-Kashi's "Tabaq al-Maneteq" II: Longitudes, Distances, and Equations of the Planets",
1194:
AL-KASHl Or AL-KASHANI, GHIYATH AL-DIN DjAMSHlD B. MASCUD B. MAHMUD, Persian mathematician and astronomer who wrote in his mother tongue and in Arabic.
1142:
1714:
600:
which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in
1062:
produced and broadcast (through
Channel 1 of IRIB) a biographical-historical film series on the life and times of Jamshid Al-Kāshi, with the title
369:. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg.
4601:
3228:
4166:
3046:
2861:
2184:
Kennedy, Edward S. (1950), "A Fifteenth-Century
Planetary Computer: al-Kashi's "Tabaq al-Manateq" I. Motion of the Sun and Moon in Longitude",
4292:
3796:
2468:
5174:
2955:
452:
places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between
1556:
4339:
3021:
2118:
920:
2368:
Mohammad K. Azarian, A summary of "Miftah al-Hisab", Missouri
Journal of Mathematical Sciences, Vol. 12, No. 2, Spring 2000, pp. 75-95
5199:
5184:
5026:
4301:
4172:
2887:
2756:
2224:
1033:
of c. 1425. Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of the
17:
3945:
2903:
2292:
2093:
1844:
1311:
791:
270:
4947:
3700:
2367:
663:(Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in a form suitable for
1222:
Al-Kāshī, or al-Kāshānī (Ghiyāth al-Dīn Jamshīd ibn Mas˓ūd al-Kāshī (al-Kāshānī)), was a
Persian mathematician and astronomer.
5179:
5088:
4779:
3721:
3471:
2324:
2054:
1398:
1076:
and produced by Mohsen Ali-Akbari. In this production, the role of the adult
Jamshid Al-Kāshi is played by Vahid Jalilvand.
1049:
arithmetic of 1527. After this, we find the triangle and the properties of binomial coefficients in several other authors."
2880:
4885:
4246:
3425:
1493:
4866:
4830:
4683:
4215:
3608:
3370:
1151:
694:
4805:
3542:
5189:
4334:
4285:
2461:
1904:
1501:
1408:
1215:
1125:
2797:
4825:
4748:
3572:
3562:
2583:
2076:
1979:
5204:
5109:
4784:
4743:
4728:
3430:
3365:
2523:
2483:
1234:
1187:
659:
1425:
4919:
3481:
274:
1013:"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by
721:
4606:
4596:
4540:
4278:
3598:
3506:
3385:
2845:
2722:
2653:
2527:
2519:
2454:
772:
465:
4324:
2970:
5194:
5169:
5041:
4161:
4040:
3914:
2960:
2628:
339:
2372:
1819:
1790:
1685:
5011:
4990:
4738:
4708:
4485:
4399:
3415:
3405:
3026:
2916:
2638:
1284:
B A Rosenfeld, A P Youschkevitch, Biography in
Dictionary of Scientific Biography (New York 1970-1990).
461:
4364:
3036:
1657:
4693:
4445:
3682:
3263:
3147:
482:
on the resolution of difficulties met by predecessors in the determination of distances and sizes of
1976:
The narrative by Latifi of the life of the celebrated
Iranian astronomer in 'The Ladder of the Sky'
1530:
4764:
4723:
4591:
4475:
3496:
3390:
3268:
3031:
2991:
2701:
2543:
2297:
1316:
1104:
956:"The introduction of decimal fractions as a common computational practice can be dated back to the
373:
Ulugh Beg described him as "a remarkable scientist" who "could solve the most difficult problems".
4450:
3486:
2313:"Kāshī: Ghiyāth (al-Milla wa-) al-Dīn Jamshīd ibn Masʿūd ibn Maḥmūd al-Kāshī [al-Kāshānī]"
2287:
2041:, as well as the distances of these to Earth. He completed this work on 1 March 1407 CE in Kashan.
1400:
The Math Book: From
Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
1306:
5133:
5128:
5118:
4425:
4420:
3501:
3450:
3112:
3102:
3041:
2692:
2500:
916:
441:
1426:"An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]"
1072:). The series, which consists of 15 parts, with each part being 45 minutes long, is directed by
5057:
4733:
4718:
4652:
4581:
3919:
3879:
3693:
3634:
3593:
3420:
3400:
3319:
3197:
2151:
727:
545:
517:
2339:
Eshera, Osama (2020). "On the Early Collections of the Works of Ġiyāṯ al-Dīn Jamšīd al-Kāšī".
2135:
1096:
874:
693:, which was the most accurate approximation of sin 1° in his time and was not surpassed until
4871:
4698:
4662:
4186:
3980:
3894:
3567:
3380:
3349:
3294:
3082:
2727:
2712:
2558:
2509:
2089:
Latifi's narrative of the life of the renowned Persian astronomer in 'The Ladder of the Sky'
1064:
782:
In order to determine sin 1°, al-Kashi discovered the following formula, often attributed to
581:
533:
4270:
984:
many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and
5164:
5159:
5036:
4985:
4861:
4840:
4713:
4621:
4205:
4179:
4020:
3990:
3395:
3375:
3066:
2965:
2950:
2669:
2659:
2588:
2538:
1026:
1002:
585:
399:
2872:
1841:
expressed exactly up to and including the 18th place after the decimal separator one has:
8:
5006:
4933:
4455:
4359:
4146:
3985:
3965:
3899:
3884:
3755:
3714:
3435:
3410:
3097:
3016:
2707:
2624:
2283:
1302:
1208:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
1138:
981:
904:
783:
483:
163:
139:
4394:
3061:
2417:"A Study of Risa-la al-Watar wa'l Jaib ("The Treatise on the Chord and Sine"):Revisited"
1994:
5138:
5093:
5067:
5016:
4657:
4535:
4470:
4210:
4151:
3829:
3781:
3639:
3192:
2986:
2416:
2400:
2356:
2271:
2241:
2211:
2173:
928:
912:
717:
702:
135:
2097:
1941:
Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection
1459:
1146:
5083:
5062:
4500:
4389:
4241:
4236:
4110:
3970:
3511:
3445:
3440:
3157:
2824:
2780:
2732:
2678:
2609:
2360:
2320:
2275:
2203:
2177:
2112:
1900:
1813:
1497:
1404:
1211:
1183:
1119:
945:
896:
453:
425:
159:
2215:
471:
4961:
4835:
4515:
4495:
4404:
4384:
4369:
4251:
4220:
4095:
4085:
4015:
3874:
3834:
3819:
3742:
3707:
3687:
3629:
3552:
3532:
3258:
3107:
2996:
2717:
2649:
2348:
2332:
2312:
2263:
2233:
2195:
2165:
2010:
1471:
1440:
895:
places of accuracy. This was far more accurate than the estimates earlier given in
706:
617:
521:
457:
243:
1444:
5122:
5114:
5021:
4774:
4637:
4556:
4440:
4156:
4090:
3854:
3809:
3339:
3213:
3182:
3132:
3117:
2945:
2742:
2664:
2060:
2018:
1046:
949:
650:
597:
577:
413:
198:
3172:
1260:
1006:
4954:
4926:
4667:
4566:
4561:
4510:
4379:
4349:
4000:
3975:
3761:
3624:
3278:
3253:
3238:
3223:
3187:
3056:
2786:
2737:
2674:
2644:
2614:
2553:
2377:
2254:
2186:
2156:
957:
768:
710:
654:
479:
328:
188:
178:
2432:
2401:"A Study of Risa-la al-Watar wa'l Jaib ("The Treatise on the Chord and Sine")"
2384:
2352:
1780:{\displaystyle \scriptstyle 1/60^{9}\approx 9.92\times 10^{-17}<10^{-16}\,}
5153:
4769:
4688:
4329:
4120:
4030:
3904:
3774:
3767:
3466:
3334:
3248:
2697:
1164:
1038:
664:
404:
4642:
3309:
2025:(رسالهٌ كماليه), Jamshid Kashani discusses such matters as the diameters of
927:
14th Century ). The accuracy of al-Kashi's estimate was not surpassed until
4800:
4616:
4374:
3950:
3844:
3557:
3491:
3344:
3087:
3051:
2816:
2772:
2634:
2573:
2515:
2207:
1018:
973:
338:
The situation changed for the better when Timur died in 1405, and his son,
305:
51:
2222:
Kennedy, Edward S. (1951), "An Islamic Computer for Planetary Latitudes",
1518:, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256
4912:
4856:
4611:
4576:
4505:
4125:
4115:
4080:
3889:
3869:
3748:
3588:
3324:
3273:
3233:
3001:
2805:
2686:
2619:
2568:
2563:
2378:
Sources relating to Ghiyath al-Din Kashani, or al-Kashi, by Jan Hogendijk
1042:
1034:
985:
977:
908:
884:
549:
445:
421:
366:
362:
266:
114:
724:. Al-Kāshī improved on this by using a form of Newton's method to solve
312:
4820:
4647:
4520:
4490:
4465:
4460:
4070:
4060:
4050:
3955:
3935:
3859:
3527:
3476:
3314:
3304:
3142:
3137:
3122:
2548:
689:, al-Kashi computed sin 1° to nearly as much accuracy as his value for
429:
224:
2446:
2245:
564:
instrument he invented, and a small armillary sphere incorporating an
4815:
4703:
4571:
4530:
4480:
4435:
4430:
4354:
4105:
4045:
3824:
3603:
3547:
3218:
3152:
3127:
3011:
2682:
2593:
2533:
601:
553:
505:
417:
361:
which soon became a prominent university. Students from all over the
358:
354:
343:
278:
262:
110:
2433:"The Introduction of Al-Risala al-Muhitiyya: An English Translation"
2017:(سُلّمُ السَماء) of a scientific work by Jamshid Kashani written in
1643:{\displaystyle \scriptstyle 59/60^{n+1}+59/60^{n+2}+\dots =1/60^{n}}
1475:
1029:
were discussed by the Persian mathematician Jamshid Al-Kāshī in his
516:, which described a variety of different instruments, including the
4586:
4525:
4344:
4130:
4100:
4065:
4055:
3995:
3814:
3329:
3299:
3243:
3177:
3167:
3092:
3006:
2267:
2237:
2199:
2169:
1014:
629:
625:
621:
565:
561:
529:
433:
347:
1490:
Sherlock Holmes in Babylon and Other Tales of Mathematical History
288:
and still, even the extant work, remains unpublished in any form.
5031:
4035:
4025:
3960:
3909:
3849:
3839:
3804:
3162:
2577:
1651:
900:
892:
698:
557:
541:
525:
473:
Astronomical Treatise on the size and distance of heavenly bodies
449:
204:
4906:
The Compendious Book on Calculation by Completion and Balancing
4010:
4005:
1487:
1470:(4), Society for Industrial and Applied Mathematics: 531–551 ,
965:
613:
324:
285:
254:
201:
84:
4300:
4075:
3940:
3864:
2038:
2026:
1022:
633:
499:
487:
437:
332:
125:
713:, which was not discovered in Europe until centuries later.
2902:
2073:
Dr Velāyati: 'The Ladder of the Sky' is faithful to history
2063:. Here the name "Latifi" is incorrectly written as "Seifi".
2034:
1876:{\displaystyle \scriptstyle 6.283\,185\,307\,179\,586\,476}
1059:
849:{\displaystyle \sin 3\phi =3\sin \phi -4\sin ^{3}\phi \,\!}
609:
537:
491:
258:
149:
88:
4968:
3733:
2030:
1488:
Marlow Anderson, Victor J. Katz, Robin J. Wilson (2004),
605:
495:
390:
353:
Eight years after he came into power in 1409, their son,
1932:, III (Cambridge University Press, New York, 1959), 135.
1182:(2. impression. ed.). Leiden : Brill. p. 702.
1005:, known in Persia as "Khayyam's triangle" (named after
878:
173:
4941:
Book on the Measurement of Plane and Spherical Figures
2051:
The programmes of the Holy month of Ramadan, Channel 1
1848:
1823:
1794:
1718:
1689:
1661:
1560:
1534:
580:
instrument used to determine the time of day at which
2440:
International Journal of Pure and Applied Mathematics
2392:
International Journal of Pure and Applied Mathematics
1991:
IRIB to spice up Ramadan evenings with special series
1847:
1822:
1812:
exactly up to and including the 16th place after the
1793:
1717:
1688:
1660:
1559:
1533:
1460:"Historical Development of the Newton-Raphson Method"
1094:
980:. It is true that decimal fractions were used by the
794:
730:
1147:
al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʿūd
887:
digits in 1424, and he converted this estimate of 2
2091:, in Persian, Mehr News Agency, 29 December 2008,
1875:
1833:
1804:
1779:
1699:
1674:
1642:
1541:
848:
755:
514:Treatise on Astronomical Observational Instruments
507:Treatise on Astronomical Observational Instruments
346:, a Turkish princess, were very interested in the
2281:
1403:. Sterling Publishing Company, Inc. p. 106.
1300:
845:
678:
5151:
2075:, in Persian, Āftāb, Tuesday, 1 September 2009,
1899:(Princeton University Press, New Jersey, 1986).
628:of the Sun. The instrument also incorporated an
576:Al-Kashi invented the Plate of Conjunctions, an
1978:, in Persian, Āftāb, Sunday, 28 December 2008,
1527:The statement that a quantity is calculated to
1258:
342:, ascended into power. Shah Rokh and his wife,
2862:Institute for Research in Fundamental Sciences
596:Al-Kashi also invented a mechanical planetary
46:Opening bifolio of a manuscript of al-Kashi's
4286:
2888:
2462:
1891:
1889:
968:in 1585, together with a French translation,
2317:The Biographical Encyclopedia of Astronomers
2154:(1947), "Al-Kashi's Plate of Conjunctions",
1917:Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī
1549:sexagesimal digits implies that the maximal
1090:
1088:
284:Much of al-Kāshī's work was not brought to
4293:
4279:
2895:
2881:
2469:
2455:
1886:
1787:. That is to say, Al-Kashi has calculated
1353:
1351:
1296:
1294:
1292:
1290:
1210:. Berlin New York: Springer. p. 132.
976:(1548-1620), then settled in the Northern
771:, a similar method was later described by
40:
5027:Constantinople observatory of Taqi ad-Din
4302:Mathematics in the medieval Islamic world
1868:
1864:
1860:
1856:
1852:
1775:
1095:O'Connor, J.; Robertson, E. (July 1999).
1085:
844:
2315:. In Thomas Hockey; et al. (eds.).
2288:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
2225:Journal of the American Oriental Society
1396:
1307:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
1259:Dold-Samplonius, Yvonne (18 June 2023).
1177:
1097:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
858:
675:or "The Treatise on the Circumference".
571:
311:
295:
2904:Astronomy in the medieval Islamic world
2476:
2430:
2414:
2398:
2382:
2310:
2293:MacTutor History of Mathematics Archive
2251:
2232:(1), American Oriental Society: 13–21,
2221:
2183:
2150:
2021:. In this work, which is also known as
1423:
1384:
1371:
1358:
1348:
1342:
1329:
1312:MacTutor History of Mathematics Archive
1287:
992:(Samarkand, early fifteenth century)."
624:of the Sun, Moon, and planets; and the
176:decimal determination to the 16th place
14:
5152:
4948:Encyclopedia of the Brethren of Purity
3701:Encyclopedia of the Brethren of Purity
3047:Khalid ibn Abd al‐Malik al‐Marwarrudhi
2338:
2319:. New York: Springer. pp. 613–5.
2117:: CS1 maint: archived copy as title (
1962:, II, 508-512. See also our Selection
1897:A Source Book in Mathematics 1200-1800
1553:in the calculated value is less than
1433:Mathematics Interdisciplinary Research
460:, such as the transformation from the
420:, who invited al-Kashi to work at his
331:family. This region was controlled by
236:Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī
4274:
3722:The Remaining Signs of Past Centuries
3660:
2914:
2876:
2528:Khayyam's Solution of Cubic Equations
2450:
1205:
1180:The Encyclopaedia of Islam, Volume IV
996:
716:A method algebraically equivalent to
591:
3671:
1457:
1053:
939:
865:
416:sultan and mathematician-astronomer
27:Persian astronomer and mathematician
5175:15th-century Iranian mathematicians
1494:Mathematical Association of America
1458:Ypma, Tjalling J. (December 1995),
1017:, one of the mathematicians of the
1009:), Struik notes that (p. 21):
247:
24:
1834:{\displaystyle \scriptstyle 2\pi }
1805:{\displaystyle \scriptstyle 2\pi }
1700:{\displaystyle \scriptstyle 2\pi }
1152:Dictionary of Scientific Biography
687:The Treatise on the Chord and Sine
25:
5216:
2304:
1930:Science and civilisation in China
1041:'s triangle on the title page of
988:fractions with great ease in his
644:
5200:Scholars from the Timurid Empire
5185:15th-century Iranian astronomers
4884:
2928:
2755:
2584:Najm al-Din al-Qazwini al-Katibi
2385:"Al-Kashi's Fundamental Theorem"
1993:, Tehran Times, 22 August 2009,
1675:{\displaystyle \scriptstyle n=9}
3426:Muhammad ibn Abi Bakr al‐Farisi
2915:
2081:
2066:
2044:
1999:
1984:
1969:
1952:
1935:
1922:
1909:
1682:, Al-Kashi has thus calculated
1521:
1509:
1481:
1451:
1417:
1390:
1377:
1364:
1335:
1322:
972:, by the Flemish mathematician
584:will occur, and for performing
556:observatory, a double quadrant
3915:Schema for horizontal sundials
3431:Abu Ali al-Hasan al-Marrakushi
2956:Muḥammad ibn Ibrāhīm al-Fazārī
2524:Khayyam-Saccheri quadrilateral
2341:Journal of Islamic Manuscripts
2053:, in Persian, 19 August 2009,
1542:{\displaystyle \scriptstyle n}
1397:Pickover, Clifford A. (2009).
1278:
1252:
1227:
1199:
1171:
1158:
1132:
931:computed 20 decimal places of
680:The Treatise of Chord and Sine
639:
381:
323:Al-Kashi was born in 1380, in
34:Ghiyāth al-Dīn Jamshīd Kāshānī
13:
1:
4920:Principles of Hindu Reckoning
2431:Azarian, Mohammad K. (2009).
2415:Azarian, Mohammad K. (2018).
2399:Azarian, Mohammad K. (2015).
2383:Azarian, Mohammad K. (2004).
2144:
1445:10.22052/mir.2019.167225.1110
1424:Azarian, Mohammad K. (2019).
1124:: CS1 maint: date and year (
720:was known to his predecessor
697:in the sixteenth century. In
251:Ghiyās-ud-dīn Jamshīd Kāshānī
76:
5180:Medieval Iranian astrologers
4173:Constantinople (Taqi al-Din)
2846:Iranian Mathematical Society
2136:Numerical approximations of
552:, the Fakhri sextant at the
512:In 1416, al-Kashi wrote the
466:equatorial coordinate system
448:digits (equivalent to eight
376:
291:
7:
5110:Hindu–Arabic numeral system
5042:University of al-Qarawiyyin
4162:University of al-Qarawiyyin
3366:Ibn al-Banna' al-Marrakushi
2129:
1919:(Steiner, Wiesbaden, 1951).
1037:mathematicians, and we see
10:
5221:
5012:Al-Mustansiriya University
4991:Islamic geometric patterns
4739:Shams al-Din al-Samarqandi
3661:
3406:Shams al-Din al-Samarqandi
2311:Schmidl, Petra G. (2007).
786:in the sixteenth century:
462:ecliptic coordinate system
357:, founded an institute in
5102:
5076:
5050:
4999:
4978:
4893:
4882:
4849:
4793:
4757:
4676:
4630:
4549:
4413:
4317:
4308:
4247:Medieval European science
4229:
4198:
4139:
3928:
3795:
3731:
3678:
3667:
3656:
3617:
3581:
3520:
3507:Sadr al-Shari'a al-Asghar
3459:
3358:
3287:
3264:Ibrahim ibn Said al-Sahli
3206:
3075:
2979:
2938:
2927:
2923:
2910:
2854:
2838:
2815:
2796:
2771:
2764:
2753:
2602:
2520:Khayyam-Pascal's triangle
2491:
2482:
2353:10.1163/1878464X-01302001
2013:translation of the title
952:states that (p. 7):
877:, he correctly computed 2
756:{\displaystyle x^{P}-N=0}
335:, better known as Timur.
300:Manuscript of al-Kashi's
215:
210:
194:
184:
169:
155:
145:
131:
121:
95:
72:
67:
59:
39:
32:
5190:15th-century astrologers
4765:Nizam al-Din al-Nisapuri
4724:Muhyi al-Din al-Maghribi
3497:Nizam al-Din al-Nisapuri
3391:Muhyi al-Din al-Maghribi
3032:Ali ibn Isa al-Asturlabi
2702:The Bridges Organization
2654:Langlands–Shahidi method
2629:Firoozbakht's conjecture
2544:Nizam al-Din al-Nisapuri
2298:University of St Andrews
1317:University of St Andrews
1105:University of St Andrews
1079:
777:Trigonometria Britannica
544:instrument of Urdi, the
327:, in central Iran, to a
5134:History of trigonometry
5129:Trigonometric functions
5123:Western Arabic numerals
5119:Eastern Arabic numerals
4684:Ibn al‐Ha'im al‐Ishbili
3599:Baha' al-din al-'Amili
3573:'Abd al-'Aziz al-Wafa'i
3451:Fakhr al-Din al-Akhlati
3371:Ibn al‐Ha'im al‐Ishbili
2693:Ebadollah S. Mahmoodian
1265:Encyclopedia Britannica
1206:Selin, Helaine (2008).
1178:Bosworth, C.E. (1990).
1074:Mohammad Hossein Latifi
875:numerical approximation
667:. His other work is al-
316:Last page of a copy of
248:غیاثالدین جمشید کاشانی
5205:15th-century inventors
5058:Babylonian mathematics
4749:Kamāl al-Dīn al-Fārisī
4734:Qutb al-Din al-Shirazi
4729:al-Hasan al-Marrakushi
4653:Al-Samawal al-Maghribi
4582:Abu Mansur al-Baghdadi
4325:'Abd al-Hamīd ibn Turk
3880:Navigational astrolabe
3635:Al Achsasi al Mouakket
3401:Qutb al-Din al-Shirazi
3320:Al-Samawal al-Maghribi
3269:Ibn Mu'adh al-Jayyani
3198:Abu al-Hasan al-Ahwazi
2639:Havel–Hakimi algorithm
1960:History of mathematics
1877:
1835:
1806:
1781:
1701:
1676:
1644:
1543:
1051:
994:
915:(11 decimal places by
850:
757:
582:planetary conjunctions
412:, al-Kashi thanks the
320:
309:
5084:Byzantine mathematics
4872:Ibn Hamza al-Maghribi
4699:Alam al-Din al-Hanafi
4663:Sharaf al-Din al-Tusi
4216:Hellenistic astronomy
4187:Samarkand (Ulugh Beg)
3981:Deferent and epicycle
3381:Alam al-Din al-Hanafi
3350:Sharaf al-Din al-Tusi
2992:Abu Ma'shar al-Balkhi
2728:Mohammad Mehdi Zahedi
2713:Gholamhossein Mosaheb
2559:Ayn al-Quzat Hamadani
2373:About Jamshid Kashani
1878:
1836:
1807:
1782:
1702:
1677:
1645:
1544:
1065:The Ladder of the Sky
1027:binomial coefficients
1011:
954:
907:(7 decimal places by
899:(3 decimal places by
860:The Key to Arithmetic
851:
779:, published in 1633.
758:
722:Sharaf al-Dīn al-Tūsī
572:Plate of Conjunctions
398:, which was based on
318:The Key to Arithmetic
315:
302:al-Risala al-Kamaliya
299:
5089:European mathematics
5037:Maragheh observatory
4862:Muhammad Baqir Yazdi
4841:Ibn Ghazi al-Miknasi
4714:Nasir al-Din al-Tusi
4622:Muhammad al-Baghdadi
4206:Babylonian astronomy
4021:Gravitational energy
3396:Nasir al-Din al-Tusi
3386:Najm al‐Din al‐Misri
3067:Yahya ibn Abi Mansur
2966:Mashallah ibn Athari
2951:Al-Fadl ibn Naubakht
2670:Ramin Takloo-Bighash
2660:Hamid Naderi Yeganeh
2589:Nasir al-Din al-Tusi
2539:Muhammad Baqir Yazdi
2501:Abu al-Wafa' Buzjani
2284:Robertson, Edmund F.
1845:
1820:
1791:
1715:
1686:
1658:
1557:
1531:
1303:Robertson, Edmund F.
1025:. The properties of
792:
728:
586:linear interpolation
440:. Al-Kashi produced
400:Nasir al-Din al-Tusi
388:Al-Kashi produced a
308:, dated 26 June 1520
277:during the reign of
5007:Al-Azhar University
4934:The Book of Healing
4340:Al-Ḥajjāj ibn Yūsuf
4147:Al-Azhar University
3966:Celestial mechanics
3756:Book of Fixed Stars
3715:The Book of Healing
3694:Aja'ib al-Makhluqat
3436:Ibn Ishaq al-Tunisi
3411:Zakariya al-Qazwini
3022:Al-Ḥajjāj ibn Yūsuf
3017:Abu Hanifa Dinawari
2708:Siavash Shahshahani
2625:Farideh Firoozbakht
2477:Mathematics in Iran
2424:Forum Geometricorum
2408:Forum Geometricorum
2282:O'Connor, John J.;
2023:Resāleh-ye Kamālieh
2009:coincides with the
1332:, pp. 104–107)
1301:O'Connor, John J.;
1139:A. P. Youschkevitch
905:Chinese mathematics
660:Théorème d'Al-Kashi
568:which he invented.
140:Timurid Renaissance
5195:Persian physicists
5170:People from Kashan
5139:History of algebra
5094:Indian mathematics
5068:Indian mathematics
5017:House of Knowledge
4471:Brethren of Purity
4365:Banū Mūsā brothers
4211:Egyptian astronomy
4152:House of Knowledge
3830:Astronomical clock
3640:Muhammad al-Rudani
3037:Banū Mūsā brothers
2987:Abu Ali al-Khayyat
2510:al-Kashi's theorem
2152:Kennedy, Edward S.
2059:2009-08-26 at the
1873:
1872:
1831:
1830:
1802:
1801:
1777:
1776:
1697:
1696:
1672:
1671:
1640:
1639:
1539:
1538:
1235:"Jamshid al-Kashi"
997:Khayyam's triangle
929:Ludolph van Ceulen
913:Indian mathematics
846:
753:
705:, he developed an
703:numerical analysis
592:Planetary computer
534:Mo'ayyeduddin Urdi
478:He wrote the book
454:coordinate systems
321:
310:
304:. Copy created in
136:Islamic Golden Age
50:. Copy created in
5147:
5146:
5063:Greek mathematics
4986:Alhazen's problem
4880:
4879:
4501:Ibrahim ibn Sinan
4451:Sinān ibn al-Fatḥ
4268:
4267:
4264:
4263:
4260:
4259:
4242:Chinese astronomy
4237:Byzantine science
4111:Temporal finitism
4041:Islamic cosmology
3971:Celestial spheres
3791:
3790:
3683:Arabic star names
3652:
3651:
3648:
3647:
3512:Fathullah Shirazi
3446:Al-Ashraf Umar II
3158:Ibrahim ibn Sinan
2961:Ibrāhīm al-Fazārī
2870:
2869:
2834:
2833:
2825:Maryam Mirzakhani
2781:Maryam Mirzakhani
2751:
2750:
2733:Mohsen Hashtroodi
2679:Fuzzy mathematics
2610:Maryam Mirzakhani
2326:978-0-387-31022-0
2087:Fatemeh Udbashi,
2015:Soll'am-os-Samā'
1814:decimal separator
1167:iranicaonline.org
1054:Biographical film
1031:Key to arithmetic
1003:Pascal's triangle
990:Key to arithmetic
946:decimal fractions
940:Decimal fractions
897:Greek mathematics
763:to find roots of
618:elliptical orbits
426:Islamic astronomy
233:
232:
16:(Redirected from
5212:
4962:Tabula Rogeriana
4888:
4836:Sibt al-Maridini
4496:Sinan ibn Thabit
4405:Abu Said Gorgani
4395:Thābit ibn Qurra
4385:Ishaq ibn Hunayn
4370:Hunayn ibn Ishaq
4315:
4314:
4295:
4288:
4281:
4272:
4271:
4252:Indian astronomy
4221:Indian astronomy
4189:
4182:
4175:
4096:Sublunary sphere
4086:Specific gravity
3986:Earth's rotation
3875:Mural instrument
3820:Armillary sphere
3743:Alfonsine tables
3708:Tabula Rogeriana
3688:Islamic calendar
3676:
3675:
3669:
3668:
3658:
3657:
3553:Sibt al-Maridini
3538:Jamshid al-Kashi
3259:Said al-Andalusi
3062:Thābit ibn Qurra
2997:Abu Said Gorgani
2971:Yaʿqūb ibn Ṭāriq
2925:
2924:
2912:
2911:
2897:
2890:
2883:
2874:
2873:
2769:
2768:
2765:Prize Recipients
2759:
2718:Amin Shokrollahi
2650:Freydoon Shahidi
2506:Jamshid al-Kashi
2489:
2488:
2471:
2464:
2457:
2448:
2447:
2443:
2437:
2427:
2421:
2411:
2405:
2395:
2389:
2364:
2330:
2300:
2278:
2248:
2218:
2180:
2139:
2124:
2122:
2116:
2108:
2106:
2105:
2096:. Archived from
2085:
2079:
2070:
2064:
2048:
2042:
2007:Nardebām-e Āsmān
2003:
1997:
1988:
1982:
1973:
1967:
1956:
1950:
1939:
1933:
1926:
1920:
1913:
1907:
1893:
1884:
1882:
1880:
1879:
1874:
1840:
1838:
1837:
1832:
1811:
1809:
1808:
1803:
1786:
1784:
1783:
1778:
1774:
1773:
1758:
1757:
1736:
1735:
1726:
1706:
1704:
1703:
1698:
1681:
1679:
1678:
1673:
1649:
1647:
1646:
1641:
1638:
1637:
1628:
1611:
1610:
1595:
1584:
1583:
1568:
1548:
1546:
1545:
1540:
1525:
1519:
1513:
1507:
1506:
1485:
1479:
1478:
1455:
1449:
1448:
1430:
1421:
1415:
1414:
1394:
1388:
1381:
1375:
1368:
1362:
1355:
1346:
1339:
1333:
1326:
1320:
1319:
1298:
1285:
1282:
1276:
1275:
1273:
1271:
1256:
1250:
1249:
1247:
1245:
1231:
1225:
1224:
1203:
1197:
1196:
1175:
1169:
1162:
1156:
1136:
1130:
1129:
1123:
1115:
1113:
1111:
1092:
1070:Nardebām-e Āsmān
934:
890:
881:
869:
866:Computation of 2
855:
853:
852:
847:
837:
836:
762:
760:
759:
754:
740:
739:
707:iterative method
692:
578:analog computing
522:armillary sphere
458:celestial sphere
249:
156:Main interest(s)
106:
104:
81:
78:
44:
30:
29:
21:
18:Jamshīd al-Kāshī
5220:
5219:
5215:
5214:
5213:
5211:
5210:
5209:
5150:
5149:
5148:
5143:
5115:Arabic numerals
5098:
5072:
5046:
5022:House of Wisdom
4995:
4974:
4896:
4889:
4876:
4845:
4789:
4775:Ibn al-Durayhim
4753:
4672:
4638:Jabir ibn Aflah
4626:
4557:Abu Nasr Mansur
4545:
4441:Ahmad ibn Yusuf
4409:
4304:
4299:
4269:
4256:
4225:
4194:
4185:
4178:
4171:
4157:House of Wisdom
4135:
4091:Spherical Earth
3924:
3855:Equatorial ring
3835:Celestial globe
3810:Analog computer
3787:
3782:Sullam al-sama'
3727:
3663:
3644:
3613:
3577:
3516:
3455:
3354:
3340:Jabir ibn Aflah
3283:
3214:Abu Nasr Mansur
3202:
3183:Abolfadl Harawi
3118:Ahmad ibn Yusuf
3071:
2975:
2946:Ahmad Nahavandi
2934:
2919:
2906:
2901:
2871:
2866:
2850:
2830:
2811:
2792:
2760:
2747:
2743:Amir Ali Ahmadi
2665:Esmail Babolian
2598:
2493:
2478:
2475:
2435:
2419:
2403:
2387:
2327:
2307:
2147:
2137:
2132:
2127:
2110:
2109:
2103:
2101:
2094:"Archived copy"
2092:
2086:
2082:
2071:
2067:
2061:Wayback Machine
2049:
2045:
2004:
2000:
1989:
1985:
1974:
1970:
1957:
1953:
1940:
1936:
1927:
1923:
1914:
1910:
1894:
1887:
1846:
1843:
1842:
1821:
1818:
1817:
1792:
1789:
1788:
1766:
1762:
1750:
1746:
1731:
1727:
1722:
1716:
1713:
1712:
1707:with a maximal
1687:
1684:
1683:
1659:
1656:
1655:
1633:
1629:
1624:
1600:
1596:
1591:
1573:
1569:
1564:
1558:
1555:
1554:
1532:
1529:
1528:
1526:
1522:
1514:
1510:
1504:
1496:, p. 139,
1486:
1482:
1476:10.1137/1037125
1456:
1452:
1428:
1422:
1418:
1411:
1395:
1391:
1382:
1378:
1369:
1365:
1356:
1349:
1340:
1336:
1327:
1323:
1299:
1288:
1283:
1279:
1269:
1267:
1257:
1253:
1243:
1241:
1233:
1232:
1228:
1218:
1204:
1200:
1190:
1176:
1172:
1163:
1159:
1143:B. A. Rosenfeld
1137:
1133:
1117:
1116:
1109:
1107:
1093:
1086:
1082:
1056:
1001:In considering
999:
964:, published at
942:
932:
888:
879:
871:
867:
863:
832:
828:
793:
790:
789:
735:
731:
729:
726:
725:
718:Newton's method
711:cubic equations
690:
683:
647:
642:
594:
574:
510:
484:heavenly bodies
476:
444:tables to four
436:) which taught
386:
379:
294:
261:– 22 June 1429
229:
221:
220:
185:Notable work(s)
177:
170:Notable idea(s)
117:
108:
102:
100:
91:
82:
79:
55:
48:Miftah al-Hisab
35:
28:
23:
22:
15:
12:
11:
5:
5218:
5208:
5207:
5202:
5197:
5192:
5187:
5182:
5177:
5172:
5167:
5162:
5145:
5144:
5142:
5141:
5136:
5131:
5126:
5112:
5106:
5104:
5100:
5099:
5097:
5096:
5091:
5086:
5080:
5078:
5074:
5073:
5071:
5070:
5065:
5060:
5054:
5052:
5048:
5047:
5045:
5044:
5039:
5034:
5029:
5024:
5019:
5014:
5009:
5003:
5001:
4997:
4996:
4994:
4993:
4988:
4982:
4980:
4976:
4975:
4973:
4972:
4965:
4958:
4955:Toledan Tables
4951:
4944:
4937:
4930:
4927:Book of Optics
4923:
4916:
4909:
4901:
4899:
4891:
4890:
4883:
4881:
4878:
4877:
4875:
4874:
4869:
4864:
4859:
4853:
4851:
4847:
4846:
4844:
4843:
4838:
4833:
4828:
4823:
4818:
4813:
4808:
4803:
4797:
4795:
4791:
4790:
4788:
4787:
4782:
4777:
4772:
4767:
4761:
4759:
4755:
4754:
4752:
4751:
4746:
4741:
4736:
4731:
4726:
4721:
4716:
4711:
4706:
4701:
4696:
4691:
4686:
4680:
4678:
4674:
4673:
4671:
4670:
4668:Ibn al-Yasamin
4665:
4660:
4655:
4650:
4645:
4640:
4634:
4632:
4628:
4627:
4625:
4624:
4619:
4614:
4609:
4604:
4599:
4594:
4589:
4584:
4579:
4574:
4569:
4567:Kushyar Gilani
4564:
4559:
4553:
4551:
4547:
4546:
4544:
4543:
4538:
4533:
4528:
4523:
4518:
4513:
4511:Nazif ibn Yumn
4508:
4503:
4498:
4493:
4488:
4483:
4478:
4473:
4468:
4463:
4458:
4453:
4448:
4443:
4438:
4433:
4428:
4423:
4417:
4415:
4411:
4410:
4408:
4407:
4402:
4397:
4392:
4390:Na'im ibn Musa
4387:
4382:
4380:Yusuf al-Khuri
4377:
4372:
4367:
4362:
4357:
4352:
4350:Qusta ibn Luqa
4347:
4342:
4337:
4332:
4327:
4321:
4319:
4312:
4310:Mathematicians
4306:
4305:
4298:
4297:
4290:
4283:
4275:
4266:
4265:
4262:
4261:
4258:
4257:
4255:
4254:
4249:
4244:
4239:
4233:
4231:
4227:
4226:
4224:
4223:
4218:
4213:
4208:
4202:
4200:
4196:
4195:
4193:
4192:
4191:
4190:
4183:
4176:
4164:
4159:
4154:
4149:
4143:
4141:
4137:
4136:
4134:
4133:
4128:
4123:
4118:
4113:
4108:
4103:
4098:
4093:
4088:
4083:
4078:
4073:
4068:
4063:
4058:
4053:
4048:
4043:
4038:
4033:
4028:
4023:
4018:
4013:
4008:
4003:
4001:Elliptic orbit
3998:
3993:
3988:
3983:
3978:
3976:Circular orbit
3973:
3968:
3963:
3958:
3953:
3948:
3943:
3938:
3932:
3930:
3926:
3925:
3923:
3922:
3917:
3912:
3907:
3902:
3897:
3892:
3887:
3882:
3877:
3872:
3867:
3862:
3857:
3852:
3847:
3842:
3837:
3832:
3827:
3822:
3817:
3812:
3807:
3801:
3799:
3793:
3792:
3789:
3788:
3786:
3785:
3778:
3771:
3764:
3762:Toledan Tables
3759:
3752:
3745:
3739:
3737:
3729:
3728:
3726:
3725:
3718:
3711:
3704:
3697:
3690:
3685:
3679:
3673:
3665:
3664:
3654:
3653:
3650:
3649:
3646:
3645:
3643:
3642:
3637:
3632:
3627:
3625:Yang Guangxian
3621:
3619:
3615:
3614:
3612:
3611:
3606:
3601:
3596:
3591:
3585:
3583:
3579:
3578:
3576:
3575:
3570:
3565:
3560:
3555:
3550:
3545:
3540:
3535:
3530:
3524:
3522:
3518:
3517:
3515:
3514:
3509:
3504:
3499:
3494:
3489:
3484:
3479:
3474:
3469:
3463:
3461:
3457:
3456:
3454:
3453:
3448:
3443:
3438:
3433:
3428:
3423:
3418:
3413:
3408:
3403:
3398:
3393:
3388:
3383:
3378:
3373:
3368:
3362:
3360:
3356:
3355:
3353:
3352:
3347:
3342:
3337:
3332:
3327:
3322:
3317:
3312:
3307:
3302:
3297:
3291:
3289:
3285:
3284:
3282:
3281:
3279:Ali ibn Khalaf
3276:
3271:
3266:
3261:
3256:
3254:Kushyar Gilani
3251:
3246:
3241:
3236:
3231:
3226:
3224:Ali ibn Ridwan
3221:
3216:
3210:
3208:
3204:
3203:
3201:
3200:
3195:
3190:
3188:Haseb-i Tabari
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3150:
3145:
3140:
3135:
3130:
3125:
3120:
3115:
3110:
3105:
3100:
3095:
3090:
3085:
3079:
3077:
3073:
3072:
3070:
3069:
3064:
3059:
3057:Sahl ibn Bishr
3054:
3049:
3044:
3039:
3034:
3029:
3024:
3019:
3014:
3009:
3004:
2999:
2994:
2989:
2983:
2981:
2977:
2976:
2974:
2973:
2968:
2963:
2958:
2953:
2948:
2942:
2940:
2936:
2935:
2933:
2932:
2921:
2920:
2908:
2907:
2900:
2899:
2892:
2885:
2877:
2868:
2867:
2865:
2864:
2858:
2856:
2852:
2851:
2849:
2848:
2842:
2840:
2836:
2835:
2832:
2831:
2829:
2828:
2821:
2819:
2813:
2812:
2810:
2809:
2802:
2800:
2794:
2793:
2791:
2790:
2787:Caucher Birkar
2784:
2777:
2775:
2766:
2762:
2761:
2754:
2752:
2749:
2748:
2746:
2745:
2740:
2738:Hossein Zakeri
2735:
2730:
2725:
2720:
2715:
2710:
2705:
2695:
2690:
2675:Lotfi A. Zadeh
2672:
2667:
2662:
2657:
2647:
2645:Siamak Yassemi
2642:
2632:
2622:
2617:
2615:Caucher Birkar
2612:
2606:
2604:
2600:
2599:
2597:
2596:
2591:
2586:
2581:
2571:
2566:
2561:
2556:
2554:Kushyar Gilani
2551:
2546:
2541:
2536:
2531:
2513:
2503:
2497:
2495:
2486:
2484:Mathematicians
2480:
2479:
2474:
2473:
2466:
2459:
2451:
2445:
2444:
2428:
2412:
2396:
2380:
2375:
2370:
2365:
2347:(2): 225–262.
2336:
2325:
2306:
2305:External links
2303:
2302:
2301:
2279:
2268:10.1086/349363
2249:
2238:10.2307/595221
2219:
2200:10.1086/349146
2194:(2): 180–183,
2181:
2170:10.1086/348036
2164:(1–2): 56–59,
2146:
2143:
2142:
2141:
2131:
2128:
2126:
2125:
2080:
2065:
2043:
1998:
1983:
1968:
1951:
1934:
1921:
1908:
1885:
1871:
1867:
1863:
1859:
1855:
1851:
1829:
1826:
1800:
1797:
1772:
1769:
1765:
1761:
1756:
1753:
1749:
1745:
1742:
1739:
1734:
1730:
1725:
1721:
1695:
1692:
1670:
1667:
1664:
1636:
1632:
1627:
1623:
1620:
1617:
1614:
1609:
1606:
1603:
1599:
1594:
1590:
1587:
1582:
1579:
1576:
1572:
1567:
1563:
1537:
1520:
1508:
1502:
1480:
1450:
1416:
1409:
1389:
1376:
1363:
1347:
1334:
1321:
1286:
1277:
1251:
1239:Scientific Lib
1226:
1216:
1198:
1188:
1170:
1157:
1131:
1083:
1081:
1078:
1055:
1052:
998:
995:
944:In discussing
941:
938:
870:
864:
862:
857:
843:
840:
835:
831:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
784:François Viète
769:western Europe
752:
749:
746:
743:
738:
734:
682:
677:
655:law of cosines
646:
645:Law of cosines
643:
641:
638:
593:
590:
573:
570:
528:armillary and
509:
504:
486:, such as the
480:Sullam al-Sama
475:
470:
385:
380:
378:
375:
293:
290:
231:
230:
228:
227:
218:
217:
216:
213:
212:
208:
207:
196:
192:
191:
189:Sullam al-Sama
186:
182:
181:
179:Law of cosines
171:
167:
166:
157:
153:
152:
147:
143:
142:
133:
129:
128:
123:
119:
118:
109:
107:(aged 48)
97:
93:
92:
83:
74:
70:
69:
65:
64:
61:
57:
56:
45:
37:
36:
33:
26:
9:
6:
4:
3:
2:
5217:
5206:
5203:
5201:
5198:
5196:
5193:
5191:
5188:
5186:
5183:
5181:
5178:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5157:
5155:
5140:
5137:
5135:
5132:
5130:
5127:
5124:
5120:
5116:
5113:
5111:
5108:
5107:
5105:
5101:
5095:
5092:
5090:
5087:
5085:
5082:
5081:
5079:
5075:
5069:
5066:
5064:
5061:
5059:
5056:
5055:
5053:
5049:
5043:
5040:
5038:
5035:
5033:
5030:
5028:
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5004:
5002:
4998:
4992:
4989:
4987:
4984:
4983:
4981:
4977:
4971:
4970:
4966:
4964:
4963:
4959:
4957:
4956:
4952:
4950:
4949:
4945:
4943:
4942:
4938:
4936:
4935:
4931:
4929:
4928:
4924:
4922:
4921:
4917:
4915:
4914:
4910:
4908:
4907:
4903:
4902:
4900:
4898:
4892:
4887:
4873:
4870:
4868:
4865:
4863:
4860:
4858:
4855:
4854:
4852:
4848:
4842:
4839:
4837:
4834:
4832:
4829:
4827:
4824:
4822:
4819:
4817:
4814:
4812:
4809:
4807:
4804:
4802:
4799:
4798:
4796:
4792:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4770:Ibn al-Shatir
4768:
4766:
4763:
4762:
4760:
4756:
4750:
4747:
4745:
4744:Ibn al-Banna'
4742:
4740:
4737:
4735:
4732:
4730:
4727:
4725:
4722:
4720:
4717:
4715:
4712:
4710:
4707:
4705:
4702:
4700:
4697:
4695:
4692:
4690:
4689:Ahmad al-Buni
4687:
4685:
4682:
4681:
4679:
4675:
4669:
4666:
4664:
4661:
4659:
4656:
4654:
4651:
4649:
4646:
4644:
4641:
4639:
4636:
4635:
4633:
4629:
4623:
4620:
4618:
4615:
4613:
4610:
4608:
4605:
4603:
4600:
4598:
4595:
4593:
4590:
4588:
4585:
4583:
4580:
4578:
4575:
4573:
4570:
4568:
4565:
4563:
4560:
4558:
4555:
4554:
4552:
4548:
4542:
4539:
4537:
4534:
4532:
4529:
4527:
4524:
4522:
4519:
4517:
4514:
4512:
4509:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4462:
4459:
4457:
4454:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4432:
4429:
4427:
4424:
4422:
4419:
4418:
4416:
4412:
4406:
4403:
4401:
4398:
4396:
4393:
4391:
4388:
4386:
4383:
4381:
4378:
4376:
4373:
4371:
4368:
4366:
4363:
4361:
4358:
4356:
4353:
4351:
4348:
4346:
4343:
4341:
4338:
4336:
4333:
4331:
4330:Sanad ibn Ali
4328:
4326:
4323:
4322:
4320:
4316:
4313:
4311:
4307:
4303:
4296:
4291:
4289:
4284:
4282:
4277:
4276:
4273:
4253:
4250:
4248:
4245:
4243:
4240:
4238:
4235:
4234:
4232:
4228:
4222:
4219:
4217:
4214:
4212:
4209:
4207:
4204:
4203:
4201:
4197:
4188:
4184:
4181:
4177:
4174:
4170:
4169:
4168:
4167:Observatories
4165:
4163:
4160:
4158:
4155:
4153:
4150:
4148:
4145:
4144:
4142:
4138:
4132:
4129:
4127:
4124:
4122:
4121:Triangulation
4119:
4117:
4114:
4112:
4109:
4107:
4104:
4102:
4099:
4097:
4094:
4092:
4089:
4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4052:
4049:
4047:
4044:
4042:
4039:
4037:
4034:
4032:
4031:Heliocentrism
4029:
4027:
4024:
4022:
4019:
4017:
4014:
4012:
4009:
4007:
4004:
4002:
3999:
3997:
3994:
3992:
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3964:
3962:
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3933:
3931:
3927:
3921:
3918:
3916:
3913:
3911:
3908:
3906:
3905:Shadow square
3903:
3901:
3898:
3896:
3893:
3891:
3888:
3886:
3883:
3881:
3878:
3876:
3873:
3871:
3868:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3841:
3838:
3836:
3833:
3831:
3828:
3826:
3823:
3821:
3818:
3816:
3813:
3811:
3808:
3806:
3803:
3802:
3800:
3798:
3794:
3784:
3783:
3779:
3777:
3776:
3775:Zij-i Sultani
3772:
3770:
3769:
3768:Zij-i Ilkhani
3765:
3763:
3760:
3758:
3757:
3753:
3751:
3750:
3746:
3744:
3741:
3740:
3738:
3736:
3735:
3730:
3724:
3723:
3719:
3717:
3716:
3712:
3710:
3709:
3705:
3703:
3702:
3698:
3696:
3695:
3691:
3689:
3686:
3684:
3681:
3680:
3677:
3674:
3670:
3666:
3659:
3655:
3641:
3638:
3636:
3633:
3631:
3628:
3626:
3623:
3622:
3620:
3616:
3610:
3607:
3605:
3602:
3600:
3597:
3595:
3592:
3590:
3587:
3586:
3584:
3580:
3574:
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3543:Kadızade Rumi
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3525:
3523:
3519:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3490:
3488:
3485:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3467:Ibn al-Shatir
3465:
3464:
3462:
3458:
3452:
3449:
3447:
3444:
3442:
3441:Ibn al‐Raqqam
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3412:
3409:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3363:
3361:
3357:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3335:Ibn al-Kammad
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3301:
3298:
3296:
3293:
3292:
3290:
3286:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3249:Ibn al-Saffar
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3211:
3209:
3205:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3080:
3078:
3074:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3048:
3045:
3043:
3040:
3038:
3035:
3033:
3030:
3028:
3025:
3023:
3020:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2995:
2993:
2990:
2988:
2985:
2984:
2982:
2978:
2972:
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2943:
2941:
2937:
2930:
2929:
2926:
2922:
2918:
2913:
2909:
2905:
2898:
2893:
2891:
2886:
2884:
2879:
2878:
2875:
2863:
2860:
2859:
2857:
2853:
2847:
2844:
2843:
2841:
2839:Organizations
2837:
2826:
2823:
2822:
2820:
2818:
2814:
2807:
2804:
2803:
2801:
2799:
2795:
2788:
2785:
2782:
2779:
2778:
2776:
2774:
2770:
2767:
2763:
2758:
2744:
2741:
2739:
2736:
2734:
2731:
2729:
2726:
2724:
2721:
2719:
2716:
2714:
2711:
2709:
2706:
2703:
2699:
2698:Reza Sarhangi
2696:
2694:
2691:
2688:
2684:
2680:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2655:
2651:
2648:
2646:
2643:
2640:
2636:
2633:
2630:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2607:
2605:
2601:
2595:
2592:
2590:
2587:
2585:
2582:
2579:
2575:
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2529:
2525:
2521:
2517:
2514:
2511:
2507:
2504:
2502:
2499:
2498:
2496:
2490:
2487:
2485:
2481:
2472:
2467:
2465:
2460:
2458:
2453:
2452:
2449:
2441:
2434:
2429:
2425:
2418:
2413:
2409:
2402:
2397:
2393:
2386:
2381:
2379:
2376:
2374:
2371:
2369:
2366:
2362:
2358:
2354:
2350:
2346:
2342:
2337:
2334:
2328:
2322:
2318:
2314:
2309:
2308:
2299:
2295:
2294:
2289:
2285:
2280:
2277:
2273:
2269:
2265:
2261:
2257:
2256:
2250:
2247:
2243:
2239:
2235:
2231:
2227:
2226:
2220:
2217:
2213:
2209:
2205:
2201:
2197:
2193:
2189:
2188:
2182:
2179:
2175:
2171:
2167:
2163:
2159:
2158:
2153:
2149:
2148:
2140:
2134:
2133:
2120:
2114:
2100:on 2011-07-22
2099:
2095:
2090:
2084:
2077:
2074:
2069:
2062:
2058:
2055:
2052:
2047:
2040:
2037:, and of the
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2008:
2002:
1995:
1992:
1987:
1980:
1977:
1972:
1965:
1961:
1955:
1948:
1944:
1938:
1931:
1925:
1918:
1912:
1906:
1905:0-691-02397-2
1902:
1898:
1895:D.J. Struik,
1892:
1890:
1869:
1865:
1861:
1857:
1853:
1849:
1827:
1824:
1815:
1798:
1795:
1770:
1767:
1763:
1759:
1754:
1751:
1747:
1743:
1740:
1737:
1732:
1728:
1723:
1719:
1710:
1693:
1690:
1668:
1665:
1662:
1654:system. With
1653:
1634:
1630:
1625:
1621:
1618:
1615:
1612:
1607:
1604:
1601:
1597:
1592:
1588:
1585:
1580:
1577:
1574:
1570:
1565:
1561:
1552:
1535:
1524:
1517:
1512:
1505:
1503:0-88385-546-1
1499:
1495:
1491:
1484:
1477:
1473:
1469:
1465:
1461:
1454:
1446:
1442:
1438:
1434:
1427:
1420:
1412:
1410:9781402757969
1406:
1402:
1401:
1393:
1386:
1380:
1373:
1367:
1360:
1354:
1352:
1345:, p. 56)
1344:
1338:
1331:
1325:
1318:
1314:
1313:
1308:
1304:
1297:
1295:
1293:
1291:
1281:
1266:
1262:
1255:
1240:
1236:
1230:
1223:
1219:
1217:9781402049606
1213:
1209:
1202:
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1191:
1185:
1181:
1174:
1168:
1165:
1161:
1154:
1153:
1148:
1144:
1140:
1135:
1127:
1121:
1106:
1102:
1101:Maths History
1098:
1091:
1089:
1084:
1077:
1075:
1071:
1067:
1066:
1061:
1050:
1048:
1044:
1040:
1036:
1032:
1028:
1024:
1020:
1016:
1010:
1008:
1004:
993:
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987:
983:
979:
975:
971:
967:
963:
959:
953:
951:
947:
937:
930:
926:
922:
921:Kerala School
918:
914:
911:, AD 480) or
910:
906:
902:
898:
894:
886:
882:
876:
861:
856:
841:
838:
833:
829:
825:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
787:
785:
780:
778:
774:
770:
766:
750:
747:
744:
741:
736:
732:
723:
719:
714:
712:
708:
704:
700:
696:
688:
681:
676:
674:
670:
666:
665:triangulation
662:
661:
656:
652:
637:
635:
631:
627:
623:
619:
615:
611:
607:
603:
599:
589:
587:
583:
579:
569:
567:
563:
559:
555:
551:
547:
543:
539:
535:
532:armillary of
531:
527:
523:
519:
515:
508:
503:
501:
497:
493:
489:
485:
481:
474:
469:
467:
463:
459:
455:
451:
447:
443:
439:
435:
431:
427:
423:
419:
415:
411:
407:
406:
405:Zij-i Ilkhani
401:
397:
394:entitled the
393:
392:
384:
374:
370:
368:
364:
360:
356:
351:
349:
345:
341:
336:
334:
330:
326:
319:
314:
307:
303:
298:
289:
287:
282:
280:
276:
275:mathematician
272:
268:
264:
260:
256:
252:
245:
241:
237:
226:
223:
222:
214:
211:Muslim leader
209:
206:
203:
200:
197:
193:
190:
187:
183:
180:
175:
172:
168:
165:
161:
158:
154:
151:
148:
144:
141:
137:
134:
130:
127:
124:
120:
116:
112:
98:
94:
90:
86:
75:
71:
66:
62:
58:
53:
49:
43:
38:
31:
19:
4967:
4960:
4953:
4946:
4939:
4932:
4925:
4918:
4911:
4904:
4895:Mathematical
4850:16th century
4810:
4801:Ibn al-Majdi
4794:15th century
4758:14th century
4677:13th century
4631:12th century
4617:Omar Khayyam
4550:11th century
4446:Aṣ-Ṣaidanānī
4414:10th century
4375:Al-Khwarizmi
4140:Institutions
3991:Eccentricity
3951:Astrophysics
3845:Compass rose
3780:
3773:
3766:
3754:
3747:
3732:
3720:
3713:
3706:
3699:
3692:
3558:Ibn al-Majdi
3537:
3533:Abd al‐Wajid
3492:Al-Wabkanawi
3487:Abū al‐ʿUqūl
3376:Jamal ad-Din
3345:Omar Khayyam
3173:Al-ʻIjliyyah
3148:Aṣ-Ṣaidanānī
3133:Ibn al-A'lam
3052:Al-Khwarizmi
2855:Institutions
2817:Satter Prize
2773:Fields Medal
2723:Reza Sadeghi
2635:S. L. Hakimi
2574:Al-Khwarizmi
2516:Omar Khayyam
2505:
2494:20th Century
2439:
2423:
2407:
2391:
2344:
2340:
2316:
2291:
2262:(1): 42–50,
2259:
2253:
2229:
2223:
2191:
2185:
2161:
2155:
2102:. Retrieved
2098:the original
2088:
2083:
2072:
2068:
2050:
2046:
2022:
2014:
2006:
2001:
1990:
1986:
1975:
1971:
1963:
1959:
1954:
1946:
1942:
1937:
1929:
1928:J. Needham,
1924:
1916:
1911:
1896:
1708:
1550:
1523:
1515:
1511:
1489:
1483:
1467:
1463:
1453:
1436:
1432:
1419:
1399:
1392:
1385:Kennedy 1951
1379:
1372:Kennedy 1952
1366:
1359:Kennedy 1950
1343:Kennedy 1947
1337:
1330:Kennedy 1951
1324:
1310:
1280:
1268:. Retrieved
1264:
1254:
1242:. Retrieved
1238:
1229:
1221:
1207:
1201:
1193:
1179:
1173:
1166:
1160:
1150:
1134:
1108:. Retrieved
1100:
1069:
1063:
1057:
1030:
1019:Song dynasty
1012:
1007:Omar Khayyám
1000:
989:
974:Simon Stevin
969:
961:
955:
943:
924:
872:
859:
788:
781:
776:
773:Henry Briggs
764:
715:
709:for solving
686:
684:
679:
672:
668:
658:
648:
616:in terms of
595:
575:
513:
511:
506:
477:
472:
409:
403:
395:
389:
387:
382:
371:
352:
337:
322:
317:
306:Safavid Iran
301:
283:
250:
239:
235:
234:
99:22 June 1429
54:, dated 1656
52:Safavid Iran
47:
5165:1429 deaths
5160:1380 births
4913:De Gradibus
4867:Taqi ad-Din
4857:Al-Birjandi
4831:al-Qalaṣādī
4612:Al-Isfizari
4577:Ibn al-Samh
4506:Al-Isfahani
4486:al-Uqlidisi
4456:al-Khojandi
4421:Abu al-Wafa
4360:al-Dinawari
4318:9th century
4126:Tusi couple
4116:Trepidation
4081:Salah times
4016:Geocentrism
3890:Planisphere
3870:Graph paper
3797:Instruments
3749:Huihui Lifa
3630:Ehmedê Xanî
3589:Al-Birjandi
3568:al-Kubunani
3325:Abu al-Salt
3274:Al-Isfizari
3234:Ibn al-Samh
3113:Abu al-Wafa
3098:al-Khojandi
3002:Al-Farghani
2917:Astronomers
2806:Sara Zahedi
2687:Fuzzy logic
2620:Sara Zahedi
2569:Al-Isfizari
2564:Al-Isfahani
2333:PDF version
1945:, footnote
1915:P. Luckey,
1464:SIAM Review
1270:14 November
1244:14 November
1110:14 November
1043:Peter Apian
1035:Renaissance
986:sexagesimal
978:Netherlands
909:Zu Chongzhi
903:, AD 150),
885:sexagesimal
695:Taqi al-Din
640:Mathematics
550:al-Khujandi
526:equinoctial
446:sexagesimal
422:observatory
410:Khaqani Zij
402:'s earlier
396:Khaqani Zij
383:Khaqani Zij
367:Middle East
363:Middle East
267:Transoxania
253:) (c. 1380
164:Mathematics
115:Transoxania
80: 1380
5154:Categories
5077:Influenced
5051:Influences
4821:Ali Qushji
4780:Al-Khalili
4648:Al-Khazini
4643:Al-Kharaqī
4602:al-Zarqālī
4592:al-Jayyānī
4536:al-Majriti
4521:Abu al-Jud
4491:Al-Battani
4466:Al-Saghani
4461:Al-Nayrizi
4400:al-Marwazi
4335:al-Jawharī
4230:Influenced
4199:Influences
4071:Precession
4051:Multiverse
3956:Axial tilt
3936:Almucantar
3920:Triquetrum
3860:Equatorium
3609:Takiyüddin
3482:al-Battiwi
3477:Ibn Shuayb
3472:Al-Khalili
3315:Al-Khazini
3310:Al-Kharaqī
3305:Ibn Tufail
3295:Al-Bitruji
3229:Al-Zarqālī
3193:al-Majriti
3143:Al-Saghani
3138:Al-Nayrizi
3123:al-Battani
3042:Iranshahri
3027:Al-Marwazi
2931:by century
2549:Al-Nayrizi
2145:References
2104:2009-10-04
1711:less than
1551:inaccuracy
1261:"al-Kāshī"
1189:9004057455
962:De Thiende
612:, and the
530:solsticial
518:triquetrum
498:, and the
430:university
428:) and his
271:astronomer
240:al-Kāshānī
225:Ali Qushji
219:Influenced
195:Occupation
103:1429-06-23
4826:al-Wafa'i
4816:Ulugh Beg
4719:al-Abhari
4704:Ibn Adlan
4694:Ibn Munim
4658:al-Hassar
4597:al-Nasawī
4572:Al-Biruni
4541:al-Jabali
4531:Al-Karaji
4481:Ibn Yunus
4436:Abu Kamil
4431:Al-Qabisi
4426:al-Khazin
4355:Al-Mahani
4106:Supernova
4061:Obliquity
4046:Moonlight
3946:Astrology
3825:Astrolabe
3604:Piri Reis
3594:al-Khafri
3563:al-Wafa'i
3548:Ulugh Beg
3528:Ali Kuşçu
3502:al-Jadiri
3421:al-Abhari
3219:al-Biruni
3153:Ibn Yunus
3128:Al-Qabisi
3103:al-Khazin
3012:Al-Mahani
2798:EMS Prize
2683:Fuzzy set
2594:Al-Biruni
2534:Al-Mahani
2361:248336832
2276:123582209
2178:143993402
2005:The name
1966:(Girard).
1828:π
1799:π
1768:−
1752:−
1744:×
1738:≈
1694:π
1616:⋯
1058:In 2009,
960:pamphlet
842:ϕ
839:
823:−
820:ϕ
817:
805:ϕ
799:
742:−
673:muhītīyya
669:Risāla al
657:is named
622:latitudes
602:longitude
554:Samarqand
418:Ulugh Beg
408:. In his
377:Astronomy
359:Samarkand
355:Ulugh Beg
344:Goharshad
340:Shah Rokh
333:Tamerlane
292:Biography
279:Tamerlane
269:) was an
263:Samarkand
160:Astronomy
111:Samarkand
4979:Concepts
4811:al-Kāshī
4785:al-Umawi
4587:Avicenna
4526:Al-Sijzi
4476:Ibn Sahl
4345:Al-Kindi
4180:Maragheh
4131:Universe
4101:Sunlight
4066:Parallax
4056:Muwaqqit
3996:Ecliptic
3929:Concepts
3895:Quadrant
3815:Aperture
3330:Averroes
3300:Avempace
3244:Avicenna
3178:Nastulus
3168:al-Sijzi
3093:Al-Adami
3007:Al-Kindi
2216:43217299
2208:15436217
2130:See also
2113:cite web
2057:Archived
1516:Al-Kashi
1120:cite web
1015:Yang Hui
970:La Disme
630:alhidade
626:ecliptic
598:computer
566:alhidade
562:altitude
438:theology
434:Madrasah
348:sciences
122:Religion
68:Personal
63:al-Kashi
5103:Related
5032:Madrasa
5000:Centers
4806:al-Rūmī
4709:al-Urdi
4607:ibn Hud
4562:Alhazen
4516:al-Qūhī
4036:Inertia
4026:Gravity
3961:Azimuth
3910:Sundial
3900:Sextant
3850:Dioptra
3840:Compass
3805:Alidade
3416:al-Urdi
3239:Alhazen
3163:Ma Yize
3108:al-Qūhī
3083:al-Sufi
2578:Al-jabr
2492:Before
2011:Persian
1958:Smith,
1652:decimal
1650:in the
982:Chinese
958:Flemish
917:Madhava
901:Ptolemy
893:decimal
873:In his
775:in his
699:algebra
614:planets
604:of the
558:Azimuth
546:sextant
542:versine
464:to the
456:on the
450:decimal
414:Timurid
329:Persian
244:Persian
205:scholar
199:Persian
101: (
4011:Galaxy
4006:Equant
3941:Apogee
3885:Octant
3662:Topics
2827:(2013)
2808:(2016)
2789:(2018)
2783:(2014)
2603:Modern
2359:
2323:
2274:
2246:595221
2244:
2214:
2206:
2176:
2033:, the
2029:, the
2019:Arabic
1903:
1816:. For
1500:
1407:
1214:
1186:
1047:German
1039:Pascal
966:Leyden
950:Struik
891:to 16
653:, the
651:French
620:; the
536:, the
524:, the
494:, the
490:, the
325:Kashan
286:Europe
255:Kashan
202:Muslim
146:Region
85:Kashan
4897:works
4076:Qibla
3865:Globe
3672:Works
2436:(PDF)
2420:(PDF)
2404:(PDF)
2388:(PDF)
2357:S2CID
2272:S2CID
2242:JSTOR
2212:S2CID
2174:S2CID
2039:stars
2027:Earth
1850:6.283
1709:error
1439:(1).
1429:(PDF)
1080:Notes
1023:China
883:to 9
767:. In
634:ruler
500:Stars
488:Earth
432:(see
424:(see
126:Islam
60:Title
3618:17th
3582:16th
3521:15th
3460:14th
3359:13th
3288:12th
3207:11th
3076:10th
2321:ISBN
2255:Isis
2204:PMID
2187:Isis
2157:Isis
2119:link
2035:Moon
1964:II.9
1901:ISBN
1760:<
1741:9.92
1498:ISBN
1405:ISBN
1272:2023
1246:2023
1212:ISBN
1184:ISBN
1141:and
1126:link
1112:2023
1060:IRIB
701:and
632:and
610:Moon
608:and
540:and
538:sine
520:and
492:Moon
442:sine
273:and
259:Iran
238:(or
150:Iran
96:Died
89:Iran
73:Born
4969:Zij
3734:Zij
3088:Ibn
2980:9th
2939:8th
2349:doi
2264:doi
2234:doi
2196:doi
2166:doi
2031:Sun
1943:I.3
1870:476
1866:586
1862:179
1858:307
1854:185
1472:doi
1441:doi
1145:. "
1045:'s
1021:in
919:of
830:sin
814:sin
796:sin
685:In
649:In
606:Sun
548:of
496:Sun
391:Zij
242:) (
132:Era
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2438:.
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1764:10
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2121:)
2107:.
2078:.
1996:.
1981:.
1949:.
1947:1
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1825:2
1796:2
1733:9
1724:/
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1663:n
1635:n
1626:/
1622:1
1619:=
1613:+
1608:2
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1536:n
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880:π
868:π
834:3
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811:3
808:=
802:3
765:N
751:0
748:=
745:N
737:P
733:x
691:π
671:-
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
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