286:
31:
4875:
2746:
302:
361:
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,
339:, 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.
924:
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).
1774:
30:
1637:
1870:
843:
4894:
1828:
1799:
1694:
1669:
1536:
2045:
750:
285:
4883:
1062:
354:
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
4929:
4298:
2883:
2241:
Kennedy, Edward S. (1952), "A Fifteenth-Century
Planetary Computer: al-Kashi's "Tabaq al-Maneteq" II: Longitudes, Distances, and Equations of the Planets",
1183:
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.
1131:
1703:
589:
which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in
1051:
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
358:. 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.
4590:
3217:
4155:
3035:
2850:
2173:
Kennedy, Edward S. (1950), "A Fifteenth-Century
Planetary Computer: al-Kashi's "Tabaq al-Manateq" I. Motion of the Sun and Moon in Longitude",
4281:
3785:
2457:
5163:
2944:
441:
places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between
1545:
4328:
3010:
2107:
909:
2357:
Mohammad K. Azarian, A summary of "Miftah al-Hisab", Missouri
Journal of Mathematical Sciences, Vol. 12, No. 2, Spring 2000, pp. 75-95
5188:
5173:
5015:
4290:
4161:
2876:
2745:
2213:
1022:
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
3934:
2892:
2281:
2082:
1833:
1300:
780:
259:
4936:
3689:
2356:
652:(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
1211:
Al-Kāshī, or al-Kāshānī (Ghiyāth al-Dīn Jamshīd ibn Mas˓ūd al-Kāshī (al-Kāshānī)), was a
Persian mathematician and astronomer.
5168:
5077:
4768:
3710:
3460:
2313:
2043:
1387:
1065:
and produced by Mohsen Ali-Akbari. In this production, the role of the adult
Jamshid Al-Kāshi is played by Vahid Jalilvand.
1038:
arithmetic of 1527. After this, we find the triangle and the properties of binomial coefficients in several other authors."
2869:
4874:
4235:
3414:
1482:
4855:
4819:
4672:
4204:
3597:
3359:
1140:
683:
4794:
3531:
5178:
4323:
4274:
2450:
1893:
1490:
1397:
1204:
1114:
2786:
4814:
4737:
3561:
3551:
2572:
2065:
1968:
5193:
5098:
4773:
4732:
4717:
3419:
3354:
2512:
2472:
1223:
1176:
648:
1414:
4908:
3470:
263:
1002:"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by
710:
4595:
4585:
4529:
4267:
3587:
3495:
3374:
2834:
2711:
2642:
2516:
2508:
2443:
761:
454:
4313:
2959:
5183:
5158:
5030:
4150:
4029:
3903:
2949:
2617:
328:
2361:
1808:
1779:
1674:
5000:
4979:
4727:
4697:
4474:
4388:
3404:
3394:
3015:
2905:
2627:
1273:
B A Rosenfeld, A P Youschkevitch, Biography in
Dictionary of Scientific Biography (New York 1970-1990).
450:
4353:
3025:
1646:
4682:
4434:
3671:
3252:
3136:
471:
on the resolution of difficulties met by predecessors in the determination of distances and sizes of
1965:
The narrative by Latifi of the life of the celebrated
Iranian astronomer in 'The Ladder of the Sky'
1519:
4753:
4712:
4580:
4464:
3485:
3379:
3257:
3020:
2980:
2690:
2532:
2286:
1305:
1093:
945:"The introduction of decimal fractions as a common computational practice can be dated back to the
362:
Ulugh Beg described him as "a remarkable scientist" who "could solve the most difficult problems".
4439:
3475:
2302:"Kāshī: Ghiyāth (al-Milla wa-) al-Dīn Jamshīd ibn Masʿūd ibn Maḥmūd al-Kāshī [al-Kāshānī]"
2276:
2030:, as well as the distances of these to Earth. He completed this work on 1 March 1407 CE in Kashan.
1389:
The Math Book: From
Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
1295:
5122:
5117:
5107:
4414:
4409:
3490:
3439:
3101:
3091:
3030:
2681:
2489:
905:
430:
1415:"An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]"
1061:). The series, which consists of 15 parts, with each part being 45 minutes long, is directed by
5046:
4722:
4707:
4641:
4570:
3908:
3868:
3682:
3623:
3582:
3409:
3389:
3308:
3186:
2140:
716:
534:
506:
2328:
Eshera, Osama (2020). "On the Early Collections of the Works of Ġiyāṯ al-Dīn Jamšīd al-Kāšī".
2124:
1085:
863:
682:, which was the most accurate approximation of sin 1° in his time and was not surpassed until
4860:
4687:
4651:
4175:
3969:
3883:
3556:
3369:
3338:
3283:
3071:
2716:
2701:
2547:
2498:
2078:
Latifi's narrative of the life of the renowned Persian astronomer in 'The Ladder of the Sky'
1053:
771:
In order to determine sin 1°, al-Kashi discovered the following formula, often attributed to
570:
522:
4259:
973:
many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and
5153:
5148:
5025:
4974:
4850:
4829:
4702:
4610:
4194:
4168:
4009:
3979:
3384:
3364:
3055:
2954:
2939:
2658:
2648:
2577:
2527:
1015:
991:
574:
388:
2861:
1830:
expressed exactly up to and including the 18th place after the decimal separator one has:
8:
4995:
4922:
4444:
4348:
4135:
3974:
3954:
3888:
3873:
3744:
3703:
3424:
3399:
3086:
3005:
2696:
2613:
2272:
1291:
1197:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
1127:
970:
893:
772:
472:
152:
128:
4383:
3050:
2406:"A Study of Risa-la al-Watar wa'l Jaib ("The Treatise on the Chord and Sine"):Revisited"
1983:
5127:
5082:
5056:
5005:
4646:
4524:
4459:
4199:
4140:
3818:
3770:
3628:
3181:
2975:
2405:
2389:
2345:
2260:
2230:
2200:
2162:
917:
901:
706:
691:
124:
2086:
1930:
Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection
1448:
1135:
5072:
5051:
4489:
4378:
4230:
4225:
4099:
3959:
3500:
3434:
3429:
3146:
2813:
2769:
2721:
2667:
2598:
2349:
2309:
2264:
2192:
2166:
2101:
1889:
1802:
1486:
1393:
1200:
1172:
1108:
934:
885:
442:
414:
148:
2204:
460:
4950:
4824:
4504:
4484:
4393:
4373:
4358:
4240:
4209:
4084:
4074:
4004:
3863:
3823:
3808:
3731:
3696:
3676:
3618:
3541:
3521:
3247:
3096:
2985:
2706:
2638:
2337:
2321:
2301:
2252:
2222:
2184:
2154:
1999:
1460:
1429:
884:
places of accuracy. This was far more accurate than the estimates earlier given in
695:
606:
510:
446:
232:
1433:
5111:
5103:
5010:
4763:
4626:
4545:
4429:
4145:
4079:
3843:
3798:
3328:
3202:
3171:
3121:
3106:
2934:
2731:
2653:
2049:
2007:
1035:
938:
639:
586:
566:
402:
187:
3161:
1249:
995:
4943:
4915:
4656:
4555:
4550:
4499:
4368:
4338:
3989:
3964:
3750:
3613:
3267:
3242:
3227:
3212:
3176:
3045:
2775:
2726:
2663:
2633:
2603:
2542:
2366:
2243:
2175:
2145:
946:
757:
699:
643:
468:
317:
177:
167:
2421:
2390:"A Study of Risa-la al-Watar wa'l Jaib ("The Treatise on the Chord and Sine")"
2373:
2341:
1769:{\displaystyle \scriptstyle 1/60^{9}\approx 9.92\times 10^{-17}<10^{-16}\,}
5142:
4758:
4677:
4318:
4109:
4019:
3893:
3763:
3756:
3455:
3323:
3237:
2686:
1153:
1027:
653:
393:
4631:
3298:
2014:(رسالهٌ كماليه), Jamshid Kashani discusses such matters as the diameters of
916:
14th Century ). The accuracy of al-Kashi's estimate was not surpassed until
4789:
4605:
4363:
3939:
3833:
3546:
3480:
3333:
3076:
3040:
2805:
2761:
2623:
2562:
2504:
2196:
1007:
962:
327:
The situation changed for the better when Timur died in 1405, and his son,
294:
40:
2211:
Kennedy, Edward S. (1951), "An Islamic Computer for Planetary Latitudes",
1507:, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256
4901:
4845:
4600:
4565:
4494:
4114:
4104:
4069:
3878:
3858:
3737:
3577:
3313:
3262:
3222:
2990:
2794:
2675:
2608:
2557:
2552:
2367:
Sources relating to Ghiyath al-Din Kashani, or al-Kashi, by Jan Hogendijk
1031:
1023:
974:
966:
897:
873:
538:
434:
410:
355:
351:
255:
103:
713:. Al-Kāshī improved on this by using a form of Newton's method to solve
301:
4809:
4636:
4509:
4479:
4454:
4449:
4059:
4049:
4039:
3944:
3924:
3848:
3516:
3465:
3303:
3293:
3131:
3126:
3111:
2537:
678:, al-Kashi computed sin 1° to nearly as much accuracy as his value for
418:
213:
2435:
2234:
553:
instrument he invented, and a small armillary sphere incorporating an
4804:
4692:
4560:
4519:
4469:
4424:
4419:
4343:
4094:
4034:
3813:
3592:
3536:
3207:
3141:
3116:
3000:
2671:
2582:
2522:
590:
542:
494:
406:
350:
which soon became a prominent university. Students from all over the
347:
343:
332:
267:
251:
99:
2422:"The Introduction of Al-Risala al-Muhitiyya: An English Translation"
2006:(سُلّمُ السَماء) of a scientific work by Jamshid Kashani written in
1632:{\displaystyle \scriptstyle 59/60^{n+1}+59/60^{n+2}+\dots =1/60^{n}}
1464:
1018:
were discussed by the Persian mathematician Jamshid Al-Kāshī in his
505:, which described a variety of different instruments, including the
4575:
4514:
4333:
4119:
4089:
4054:
4044:
3984:
3803:
3318:
3288:
3232:
3166:
3156:
3081:
2995:
2256:
2226:
2188:
2158:
1003:
618:
614:
610:
554:
550:
518:
422:
336:
1479:
Sherlock Holmes in Babylon and Other Tales of Mathematical History
277:
and still, even the extant work, remains unpublished in any form.
5020:
4024:
4014:
3949:
3898:
3838:
3828:
3793:
3151:
2566:
1640:
889:
881:
687:
546:
530:
514:
462:
Astronomical Treatise on the size and distance of heavenly bodies
438:
193:
4895:
The Compendious Book on Calculation by Completion and Balancing
3999:
3994:
1476:
1459:(4), Society for Industrial and Applied Mathematics: 531–551 ,
954:
602:
313:
274:
243:
190:
73:
4289:
4064:
3929:
3853:
2027:
2015:
1011:
622:
488:
476:
426:
321:
114:
702:, which was not discovered in Europe until centuries later.
2891:
2062:
Dr Velāyati: 'The Ladder of the Sky' is faithful to history
2052:. Here the name "Latifi" is incorrectly written as "Seifi".
2023:
1865:{\displaystyle \scriptstyle 6.283\,185\,307\,179\,586\,476}
1048:
838:{\displaystyle \sin 3\phi =3\sin \phi -4\sin ^{3}\phi \,\!}
598:
526:
480:
247:
138:
77:
4957:
3722:
2019:
1477:
Marlow Anderson, Victor J. Katz, Robin J. Wilson (2004),
594:
484:
379:
342:
Eight years after he came into power in 1409, their son,
1921:, III (Cambridge University Press, New York, 1959), 135.
1171:(2. impression. ed.). Leiden : Brill. p. 702.
994:, known in Persia as "Khayyam's triangle" (named after
867:
162:
4930:
Book on the Measurement of Plane and Spherical Figures
2040:
The programmes of the Holy month of Ramadan, Channel 1
1837:
1812:
1783:
1707:
1678:
1650:
1549:
1523:
569:
instrument used to determine the time of day at which
2429:
International Journal of Pure and Applied Mathematics
2381:
International Journal of Pure and Applied Mathematics
1980:
IRIB to spice up Ramadan evenings with special series
1836:
1811:
1801:
exactly up to and including the 16th place after the
1782:
1706:
1677:
1649:
1548:
1522:
1449:"Historical Development of the Newton-Raphson Method"
1083:
969:. It is true that decimal fractions were used by the
783:
719:
1136:
al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʿūd
876:
digits in 1424, and he converted this estimate of 2
2080:, in Persian, Mehr News Agency, 29 December 2008,
1864:
1822:
1793:
1768:
1688:
1663:
1631:
1530:
837:
744:
503:Treatise on Astronomical Observational Instruments
496:Treatise on Astronomical Observational Instruments
335:, a Turkish princess, were very interested in the
2270:
1392:. Sterling Publishing Company, Inc. p. 106.
1289:
834:
667:
5140:
2064:, in Persian, Āftāb, Tuesday, 1 September 2009,
1888:(Princeton University Press, New Jersey, 1986).
617:of the Sun. The instrument also incorporated an
565:Al-Kashi invented the Plate of Conjunctions, an
1967:, in Persian, Āftāb, Sunday, 28 December 2008,
1516:The statement that a quantity is calculated to
1247:
331:, ascended into power. Shah Rokh and his wife,
2851:Institute for Research in Fundamental Sciences
585:Al-Kashi also invented a mechanical planetary
35:Opening bifolio of a manuscript of al-Kashi's
4275:
2877:
2451:
1880:
1878:
957:in 1585, together with a French translation,
2306:The Biographical Encyclopedia of Astronomers
2143:(1947), "Al-Kashi's Plate of Conjunctions",
1906:Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī
1538:sexagesimal digits implies that the maximal
1079:
1077:
273:Much of al-Kāshī's work was not brought to
4282:
4268:
2884:
2870:
2458:
2444:
1875:
1776:. That is to say, Al-Kashi has calculated
1342:
1340:
1285:
1283:
1281:
1279:
1199:. Berlin New York: Springer. p. 132.
965:(1548-1620), then settled in the Northern
760:, a similar method was later described by
29:
5016:Constantinople observatory of Taqi ad-Din
4291:Mathematics in the medieval Islamic world
1857:
1853:
1849:
1845:
1841:
1764:
1084:O'Connor, J.; Robertson, E. (July 1999).
1074:
833:
2304:. In Thomas Hockey; et al. (eds.).
2277:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
2214:Journal of the American Oriental Society
1385:
1296:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
1248:Dold-Samplonius, Yvonne (18 June 2023).
1166:
1086:"Ghiyath al-Din Jamshid Mas'ud al-Kashi"
847:
664:or "The Treatise on the Circumference".
560:
300:
284:
2893:Astronomy in the medieval Islamic world
2465:
2419:
2403:
2387:
2371:
2299:
2282:MacTutor History of Mathematics Archive
2240:
2221:(1), American Oriental Society: 13–21,
2210:
2172:
2139:
2010:. In this work, which is also known as
1412:
1373:
1360:
1347:
1337:
1331:
1318:
1301:MacTutor History of Mathematics Archive
1276:
981:(Samarkand, early fifteenth century)."
613:of the Sun, Moon, and planets; and the
165:decimal determination to the 16th place
5141:
4937:Encyclopedia of the Brethren of Purity
3690:Encyclopedia of the Brethren of Purity
3036:Khalid ibn Abd al‐Malik al‐Marwarrudhi
2327:
2308:. New York: Springer. pp. 613–5.
2106:: CS1 maint: archived copy as title (
1951:, II, 508-512. See also our Selection
1886:A Source Book in Mathematics 1200-1800
1542:in the calculated value is less than
1422:Mathematics Interdisciplinary Research
449:, such as the transformation from the
409:, who invited al-Kashi to work at his
320:family. This region was controlled by
225:Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī
4263:
3711:The Remaining Signs of Past Centuries
3649:
2903:
2865:
2517:Khayyam's Solution of Cubic Equations
2439:
1194:
1169:The Encyclopaedia of Islam, Volume IV
985:
705:A method algebraically equivalent to
580:
3660:
1446:
1042:
928:
854:
405:sultan and mathematician-astronomer
16:Persian astronomer and mathematician
5164:15th-century Iranian mathematicians
1483:Mathematical Association of America
1447:Ypma, Tjalling J. (December 1995),
1006:, one of the mathematicians of the
998:), Struik notes that (p. 21):
236:
13:
1823:{\displaystyle \scriptstyle 2\pi }
1794:{\displaystyle \scriptstyle 2\pi }
1689:{\displaystyle \scriptstyle 2\pi }
1141:Dictionary of Scientific Biography
676:The Treatise on the Chord and Sine
14:
5205:
2293:
1919:Science and civilisation in China
1030:'s triangle on the title page of
977:fractions with great ease in his
633:
5189:Scholars from the Timurid Empire
5174:15th-century Iranian astronomers
4873:
2917:
2744:
2573:Najm al-Din al-Qazwini al-Katibi
2374:"Al-Kashi's Fundamental Theorem"
1982:, Tehran Times, 22 August 2009,
1664:{\displaystyle \scriptstyle n=9}
3415:Muhammad ibn Abi Bakr al‐Farisi
2904:
2070:
2055:
2033:
1988:
1973:
1958:
1941:
1924:
1911:
1898:
1671:, Al-Kashi has thus calculated
1510:
1498:
1470:
1440:
1406:
1379:
1366:
1353:
1324:
1311:
961:, by the Flemish mathematician
573:will occur, and for performing
545:observatory, a double quadrant
3904:Schema for horizontal sundials
3420:Abu Ali al-Hasan al-Marrakushi
2945:Muḥammad ibn Ibrāhīm al-Fazārī
2513:Khayyam-Saccheri quadrilateral
2330:Journal of Islamic Manuscripts
2042:, in Persian, 19 August 2009,
1531:{\displaystyle \scriptstyle n}
1386:Pickover, Clifford A. (2009).
1267:
1241:
1216:
1188:
1160:
1147:
1121:
920:computed 20 decimal places of
669:The Treatise of Chord and Sine
628:
370:
312:Al-Kashi was born in 1380, in
23:Ghiyāth al-Dīn Jamshīd Kāshānī
1:
4909:Principles of Hindu Reckoning
2420:Azarian, Mohammad K. (2009).
2404:Azarian, Mohammad K. (2018).
2388:Azarian, Mohammad K. (2015).
2372:Azarian, Mohammad K. (2004).
2133:
1434:10.22052/mir.2019.167225.1110
1413:Azarian, Mohammad K. (2019).
1113:: CS1 maint: date and year (
709:was known to his predecessor
686:in the sixteenth century. In
240:Ghiyās-ud-dīn Jamshīd Kāshānī
65:
5169:Medieval Iranian astrologers
4162:Constantinople (Taqi al-Din)
2835:Iranian Mathematical Society
2125:Numerical approximations of
541:, the Fakhri sextant at the
501:In 1416, al-Kashi wrote the
455:equatorial coordinate system
437:digits (equivalent to eight
365:
280:
7:
5099:Hindu–Arabic numeral system
5031:University of al-Qarawiyyin
4151:University of al-Qarawiyyin
3355:Ibn al-Banna' al-Marrakushi
2118:
1908:(Steiner, Wiesbaden, 1951).
1026:mathematicians, and we see
10:
5210:
5001:Al-Mustansiriya University
4980:Islamic geometric patterns
4728:Shams al-Din al-Samarqandi
3650:
3395:Shams al-Din al-Samarqandi
2300:Schmidl, Petra G. (2007).
775:in the sixteenth century:
451:ecliptic coordinate system
346:, founded an institute in
5091:
5065:
5039:
4988:
4967:
4882:
4871:
4838:
4782:
4746:
4665:
4619:
4538:
4402:
4306:
4297:
4236:Medieval European science
4218:
4187:
4128:
3917:
3784:
3720:
3667:
3656:
3645:
3606:
3570:
3509:
3496:Sadr al-Shari'a al-Asghar
3448:
3347:
3276:
3253:Ibrahim ibn Said al-Sahli
3195:
3064:
2968:
2927:
2916:
2912:
2899:
2843:
2827:
2804:
2785:
2760:
2753:
2742:
2591:
2509:Khayyam-Pascal's triangle
2480:
2471:
2342:10.1163/1878464X-01302001
2002:translation of the title
941:states that (p. 7):
866:, he correctly computed 2
745:{\displaystyle x^{P}-N=0}
324:, better known as Timur.
289:Manuscript of al-Kashi's
204:
199:
183:
173:
158:
144:
134:
120:
110:
84:
61:
56:
48:
28:
21:
5179:15th-century astrologers
4754:Nizam al-Din al-Nisapuri
4713:Muhyi al-Din al-Maghribi
3486:Nizam al-Din al-Nisapuri
3380:Muhyi al-Din al-Maghribi
3021:Ali ibn Isa al-Asturlabi
2691:The Bridges Organization
2643:Langlands–Shahidi method
2618:Firoozbakht's conjecture
2533:Nizam al-Din al-Nisapuri
2287:University of St Andrews
1306:University of St Andrews
1094:University of St Andrews
1068:
766:Trigonometria Britannica
533:instrument of Urdi, the
316:, in central Iran, to a
5123:History of trigonometry
5118:Trigonometric functions
5112:Western Arabic numerals
5108:Eastern Arabic numerals
4673:Ibn al‐Ha'im al‐Ishbili
3588:Baha' al-din al-'Amili
3562:'Abd al-'Aziz al-Wafa'i
3440:Fakhr al-Din al-Akhlati
3360:Ibn al‐Ha'im al‐Ishbili
2682:Ebadollah S. Mahmoodian
1254:Encyclopedia Britannica
1195:Selin, Helaine (2008).
1167:Bosworth, C.E. (1990).
1063:Mohammad Hossein Latifi
864:numerical approximation
656:. His other work is al-
305:Last page of a copy of
237:غیاث الدین جمشید کاشانی
5194:15th-century inventors
5047:Babylonian mathematics
4738:Kamāl al-Dīn al-Fārisī
4723:Qutb al-Din al-Shirazi
4718:al-Hasan al-Marrakushi
4642:Al-Samawal al-Maghribi
4571:Abu Mansur al-Baghdadi
4314:'Abd al-Hamīd ibn Turk
3869:Navigational astrolabe
3624:Al Achsasi al Mouakket
3390:Qutb al-Din al-Shirazi
3309:Al-Samawal al-Maghribi
3258:Ibn Mu'adh al-Jayyani
3187:Abu al-Hasan al-Ahwazi
2628:Havel–Hakimi algorithm
1949:History of mathematics
1866:
1824:
1795:
1770:
1690:
1665:
1633:
1532:
1040:
983:
904:(11 decimal places by
839:
746:
571:planetary conjunctions
401:, al-Kashi thanks the
309:
298:
5073:Byzantine mathematics
4861:Ibn Hamza al-Maghribi
4688:Alam al-Din al-Hanafi
4652:Sharaf al-Din al-Tusi
4205:Hellenistic astronomy
4176:Samarkand (Ulugh Beg)
3970:Deferent and epicycle
3370:Alam al-Din al-Hanafi
3339:Sharaf al-Din al-Tusi
2981:Abu Ma'shar al-Balkhi
2717:Mohammad Mehdi Zahedi
2702:Gholamhossein Mosaheb
2548:Ayn al-Quzat Hamadani
2362:About Jamshid Kashani
1867:
1825:
1796:
1771:
1691:
1666:
1634:
1533:
1054:The Ladder of the Sky
1016:binomial coefficients
1000:
943:
896:(7 decimal places by
888:(3 decimal places by
849:The Key to Arithmetic
840:
768:, published in 1633.
747:
711:Sharaf al-Dīn al-Tūsī
561:Plate of Conjunctions
387:, which was based on
307:The Key to Arithmetic
304:
291:al-Risala al-Kamaliya
288:
5078:European mathematics
5026:Maragheh observatory
4851:Muhammad Baqir Yazdi
4830:Ibn Ghazi al-Miknasi
4703:Nasir al-Din al-Tusi
4611:Muhammad al-Baghdadi
4195:Babylonian astronomy
4010:Gravitational energy
3385:Nasir al-Din al-Tusi
3375:Najm al‐Din al‐Misri
3056:Yahya ibn Abi Mansur
2955:Mashallah ibn Athari
2940:Al-Fadl ibn Naubakht
2659:Ramin Takloo-Bighash
2649:Hamid Naderi Yeganeh
2578:Nasir al-Din al-Tusi
2528:Muhammad Baqir Yazdi
2490:Abu al-Wafa' Buzjani
2273:Robertson, Edmund F.
1834:
1809:
1780:
1704:
1675:
1647:
1546:
1520:
1292:Robertson, Edmund F.
1014:. The properties of
781:
717:
575:linear interpolation
429:. Al-Kashi produced
389:Nasir al-Din al-Tusi
377:Al-Kashi produced a
297:, dated 26 June 1520
266:during the reign of
4996:Al-Azhar University
4923:The Book of Healing
4329:Al-Ḥajjāj ibn Yūsuf
4136:Al-Azhar University
3955:Celestial mechanics
3745:Book of Fixed Stars
3704:The Book of Healing
3683:Aja'ib al-Makhluqat
3425:Ibn Ishaq al-Tunisi
3400:Zakariya al-Qazwini
3011:Al-Ḥajjāj ibn Yūsuf
3006:Abu Hanifa Dinawari
2697:Siavash Shahshahani
2614:Farideh Firoozbakht
2466:Mathematics in Iran
2413:Forum Geometricorum
2397:Forum Geometricorum
2271:O'Connor, John J.;
2012:Resāleh-ye Kamālieh
1998:coincides with the
1321:, pp. 104–107)
1290:O'Connor, John J.;
1128:A. P. Youschkevitch
894:Chinese mathematics
649:Théorème d'Al-Kashi
557:which he invented.
129:Timurid Renaissance
5184:Persian physicists
5159:People from Kashan
5128:History of algebra
5083:Indian mathematics
5057:Indian mathematics
5006:House of Knowledge
4460:Brethren of Purity
4354:Banū Mūsā brothers
4200:Egyptian astronomy
4141:House of Knowledge
3819:Astronomical clock
3629:Muhammad al-Rudani
3026:Banū Mūsā brothers
2976:Abu Ali al-Khayyat
2499:al-Kashi's theorem
2141:Kennedy, Edward S.
2048:2009-08-26 at the
1862:
1861:
1820:
1819:
1791:
1790:
1766:
1765:
1686:
1685:
1661:
1660:
1629:
1628:
1528:
1527:
1224:"Jamshid al-Kashi"
986:Khayyam's triangle
918:Ludolph van Ceulen
902:Indian mathematics
835:
742:
694:, he developed an
692:numerical analysis
581:Planetary computer
523:Mo'ayyeduddin Urdi
467:He wrote the book
443:coordinate systems
310:
299:
293:. Copy created in
125:Islamic Golden Age
39:. Copy created in
5136:
5135:
5052:Greek mathematics
4975:Alhazen's problem
4869:
4868:
4490:Ibrahim ibn Sinan
4440:Sinān ibn al-Fatḥ
4257:
4256:
4253:
4252:
4249:
4248:
4231:Chinese astronomy
4226:Byzantine science
4100:Temporal finitism
4030:Islamic cosmology
3960:Celestial spheres
3780:
3779:
3672:Arabic star names
3641:
3640:
3637:
3636:
3501:Fathullah Shirazi
3435:Al-Ashraf Umar II
3147:Ibrahim ibn Sinan
2950:Ibrāhīm al-Fazārī
2859:
2858:
2823:
2822:
2814:Maryam Mirzakhani
2770:Maryam Mirzakhani
2740:
2739:
2722:Mohsen Hashtroodi
2668:Fuzzy mathematics
2599:Maryam Mirzakhani
2315:978-0-387-31022-0
2076:Fatemeh Udbashi,
2004:Soll'am-os-Samā'
1803:decimal separator
1156:iranicaonline.org
1043:Biographical film
1020:Key to arithmetic
992:Pascal's triangle
979:Key to arithmetic
935:decimal fractions
929:Decimal fractions
886:Greek mathematics
752:to find roots of
607:elliptical orbits
415:Islamic astronomy
222:
221:
5201:
4951:Tabula Rogeriana
4877:
4825:Sibt al-Maridini
4485:Sinan ibn Thabit
4394:Abu Said Gorgani
4384:Thābit ibn Qurra
4374:Ishaq ibn Hunayn
4359:Hunayn ibn Ishaq
4304:
4303:
4284:
4277:
4270:
4261:
4260:
4241:Indian astronomy
4210:Indian astronomy
4178:
4171:
4164:
4085:Sublunary sphere
4075:Specific gravity
3975:Earth's rotation
3864:Mural instrument
3809:Armillary sphere
3732:Alfonsine tables
3697:Tabula Rogeriana
3677:Islamic calendar
3665:
3664:
3658:
3657:
3647:
3646:
3542:Sibt al-Maridini
3527:Jamshid al-Kashi
3248:Said al-Andalusi
3051:Thābit ibn Qurra
2986:Abu Said Gorgani
2960:Yaʿqūb ibn Ṭāriq
2914:
2913:
2901:
2900:
2886:
2879:
2872:
2863:
2862:
2758:
2757:
2754:Prize Recipients
2748:
2707:Amin Shokrollahi
2639:Freydoon Shahidi
2495:Jamshid al-Kashi
2478:
2477:
2460:
2453:
2446:
2437:
2436:
2432:
2426:
2416:
2410:
2400:
2394:
2384:
2378:
2353:
2319:
2289:
2267:
2237:
2207:
2169:
2128:
2113:
2111:
2105:
2097:
2095:
2094:
2085:. Archived from
2074:
2068:
2059:
2053:
2037:
2031:
1996:Nardebām-e Āsmān
1992:
1986:
1977:
1971:
1962:
1956:
1945:
1939:
1928:
1922:
1915:
1909:
1902:
1896:
1882:
1873:
1871:
1869:
1868:
1863:
1829:
1827:
1826:
1821:
1800:
1798:
1797:
1792:
1775:
1773:
1772:
1767:
1763:
1762:
1747:
1746:
1725:
1724:
1715:
1695:
1693:
1692:
1687:
1670:
1668:
1667:
1662:
1638:
1636:
1635:
1630:
1627:
1626:
1617:
1600:
1599:
1584:
1573:
1572:
1557:
1537:
1535:
1534:
1529:
1514:
1508:
1502:
1496:
1495:
1474:
1468:
1467:
1444:
1438:
1437:
1419:
1410:
1404:
1403:
1383:
1377:
1370:
1364:
1357:
1351:
1344:
1335:
1328:
1322:
1315:
1309:
1308:
1287:
1274:
1271:
1265:
1264:
1262:
1260:
1245:
1239:
1238:
1236:
1234:
1220:
1214:
1213:
1192:
1186:
1185:
1164:
1158:
1151:
1145:
1125:
1119:
1118:
1112:
1104:
1102:
1100:
1081:
1059:Nardebām-e Āsmān
923:
879:
870:
858:
855:Computation of 2
844:
842:
841:
836:
826:
825:
751:
749:
748:
743:
729:
728:
696:iterative method
681:
567:analog computing
511:armillary sphere
447:celestial sphere
238:
145:Main interest(s)
95:
93:
70:
67:
33:
19:
18:
5209:
5208:
5204:
5203:
5202:
5200:
5199:
5198:
5139:
5138:
5137:
5132:
5104:Arabic numerals
5087:
5061:
5035:
5011:House of Wisdom
4984:
4963:
4885:
4878:
4865:
4834:
4778:
4764:Ibn al-Durayhim
4742:
4661:
4627:Jabir ibn Aflah
4615:
4546:Abu Nasr Mansur
4534:
4430:Ahmad ibn Yusuf
4398:
4293:
4288:
4258:
4245:
4214:
4183:
4174:
4167:
4160:
4146:House of Wisdom
4124:
4080:Spherical Earth
3913:
3844:Equatorial ring
3824:Celestial globe
3799:Analog computer
3776:
3771:Sullam al-sama'
3716:
3652:
3633:
3602:
3566:
3505:
3444:
3343:
3329:Jabir ibn Aflah
3272:
3203:Abu Nasr Mansur
3191:
3172:Abolfadl Harawi
3107:Ahmad ibn Yusuf
3060:
2964:
2935:Ahmad Nahavandi
2923:
2908:
2895:
2890:
2860:
2855:
2839:
2819:
2800:
2781:
2749:
2736:
2732:Amir Ali Ahmadi
2654:Esmail Babolian
2587:
2482:
2467:
2464:
2424:
2408:
2392:
2376:
2316:
2296:
2136:
2126:
2121:
2116:
2099:
2098:
2092:
2090:
2083:"Archived copy"
2081:
2075:
2071:
2060:
2056:
2050:Wayback Machine
2038:
2034:
1993:
1989:
1978:
1974:
1963:
1959:
1946:
1942:
1929:
1925:
1916:
1912:
1903:
1899:
1883:
1876:
1835:
1832:
1831:
1810:
1807:
1806:
1781:
1778:
1777:
1755:
1751:
1739:
1735:
1720:
1716:
1711:
1705:
1702:
1701:
1696:with a maximal
1676:
1673:
1672:
1648:
1645:
1644:
1622:
1618:
1613:
1589:
1585:
1580:
1562:
1558:
1553:
1547:
1544:
1543:
1521:
1518:
1517:
1515:
1511:
1503:
1499:
1493:
1485:, p. 139,
1475:
1471:
1465:10.1137/1037125
1445:
1441:
1417:
1411:
1407:
1400:
1384:
1380:
1371:
1367:
1358:
1354:
1345:
1338:
1329:
1325:
1316:
1312:
1288:
1277:
1272:
1268:
1258:
1256:
1246:
1242:
1232:
1230:
1222:
1221:
1217:
1207:
1193:
1189:
1179:
1165:
1161:
1152:
1148:
1132:B. A. Rosenfeld
1126:
1122:
1106:
1105:
1098:
1096:
1082:
1075:
1071:
1045:
990:In considering
988:
953:, published at
931:
921:
877:
868:
860:
856:
852:
821:
817:
782:
779:
778:
724:
720:
718:
715:
714:
707:Newton's method
700:cubic equations
679:
672:
636:
631:
583:
563:
499:
473:heavenly bodies
465:
433:tables to four
425:) which taught
375:
368:
283:
250:– 22 June 1429
218:
210:
209:
174:Notable work(s)
166:
159:Notable idea(s)
106:
97:
91:
89:
80:
71:
68:
44:
37:Miftah al-Hisab
24:
17:
12:
11:
5:
5207:
5197:
5196:
5191:
5186:
5181:
5176:
5171:
5166:
5161:
5156:
5151:
5134:
5133:
5131:
5130:
5125:
5120:
5115:
5101:
5095:
5093:
5089:
5088:
5086:
5085:
5080:
5075:
5069:
5067:
5063:
5062:
5060:
5059:
5054:
5049:
5043:
5041:
5037:
5036:
5034:
5033:
5028:
5023:
5018:
5013:
5008:
5003:
4998:
4992:
4990:
4986:
4985:
4983:
4982:
4977:
4971:
4969:
4965:
4964:
4962:
4961:
4954:
4947:
4944:Toledan Tables
4940:
4933:
4926:
4919:
4916:Book of Optics
4912:
4905:
4898:
4890:
4888:
4880:
4879:
4872:
4870:
4867:
4866:
4864:
4863:
4858:
4853:
4848:
4842:
4840:
4836:
4835:
4833:
4832:
4827:
4822:
4817:
4812:
4807:
4802:
4797:
4792:
4786:
4784:
4780:
4779:
4777:
4776:
4771:
4766:
4761:
4756:
4750:
4748:
4744:
4743:
4741:
4740:
4735:
4730:
4725:
4720:
4715:
4710:
4705:
4700:
4695:
4690:
4685:
4680:
4675:
4669:
4667:
4663:
4662:
4660:
4659:
4657:Ibn al-Yasamin
4654:
4649:
4644:
4639:
4634:
4629:
4623:
4621:
4617:
4616:
4614:
4613:
4608:
4603:
4598:
4593:
4588:
4583:
4578:
4573:
4568:
4563:
4558:
4556:Kushyar Gilani
4553:
4548:
4542:
4540:
4536:
4535:
4533:
4532:
4527:
4522:
4517:
4512:
4507:
4502:
4500:Nazif ibn Yumn
4497:
4492:
4487:
4482:
4477:
4472:
4467:
4462:
4457:
4452:
4447:
4442:
4437:
4432:
4427:
4422:
4417:
4412:
4406:
4404:
4400:
4399:
4397:
4396:
4391:
4386:
4381:
4379:Na'im ibn Musa
4376:
4371:
4369:Yusuf al-Khuri
4366:
4361:
4356:
4351:
4346:
4341:
4339:Qusta ibn Luqa
4336:
4331:
4326:
4321:
4316:
4310:
4308:
4301:
4299:Mathematicians
4295:
4294:
4287:
4286:
4279:
4272:
4264:
4255:
4254:
4251:
4250:
4247:
4246:
4244:
4243:
4238:
4233:
4228:
4222:
4220:
4216:
4215:
4213:
4212:
4207:
4202:
4197:
4191:
4189:
4185:
4184:
4182:
4181:
4180:
4179:
4172:
4165:
4153:
4148:
4143:
4138:
4132:
4130:
4126:
4125:
4123:
4122:
4117:
4112:
4107:
4102:
4097:
4092:
4087:
4082:
4077:
4072:
4067:
4062:
4057:
4052:
4047:
4042:
4037:
4032:
4027:
4022:
4017:
4012:
4007:
4002:
3997:
3992:
3990:Elliptic orbit
3987:
3982:
3977:
3972:
3967:
3965:Circular orbit
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3927:
3921:
3919:
3915:
3914:
3912:
3911:
3906:
3901:
3896:
3891:
3886:
3881:
3876:
3871:
3866:
3861:
3856:
3851:
3846:
3841:
3836:
3831:
3826:
3821:
3816:
3811:
3806:
3801:
3796:
3790:
3788:
3782:
3781:
3778:
3777:
3775:
3774:
3767:
3760:
3753:
3751:Toledan Tables
3748:
3741:
3734:
3728:
3726:
3718:
3717:
3715:
3714:
3707:
3700:
3693:
3686:
3679:
3674:
3668:
3662:
3654:
3653:
3643:
3642:
3639:
3638:
3635:
3634:
3632:
3631:
3626:
3621:
3616:
3614:Yang Guangxian
3610:
3608:
3604:
3603:
3601:
3600:
3595:
3590:
3585:
3580:
3574:
3572:
3568:
3567:
3565:
3564:
3559:
3554:
3549:
3544:
3539:
3534:
3529:
3524:
3519:
3513:
3511:
3507:
3506:
3504:
3503:
3498:
3493:
3488:
3483:
3478:
3473:
3468:
3463:
3458:
3452:
3450:
3446:
3445:
3443:
3442:
3437:
3432:
3427:
3422:
3417:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3377:
3372:
3367:
3362:
3357:
3351:
3349:
3345:
3344:
3342:
3341:
3336:
3331:
3326:
3321:
3316:
3311:
3306:
3301:
3296:
3291:
3286:
3280:
3278:
3274:
3273:
3271:
3270:
3268:Ali ibn Khalaf
3265:
3260:
3255:
3250:
3245:
3243:Kushyar Gilani
3240:
3235:
3230:
3225:
3220:
3215:
3213:Ali ibn Ridwan
3210:
3205:
3199:
3197:
3193:
3192:
3190:
3189:
3184:
3179:
3177:Haseb-i Tabari
3174:
3169:
3164:
3159:
3154:
3149:
3144:
3139:
3134:
3129:
3124:
3119:
3114:
3109:
3104:
3099:
3094:
3089:
3084:
3079:
3074:
3068:
3066:
3062:
3061:
3059:
3058:
3053:
3048:
3046:Sahl ibn Bishr
3043:
3038:
3033:
3028:
3023:
3018:
3013:
3008:
3003:
2998:
2993:
2988:
2983:
2978:
2972:
2970:
2966:
2965:
2963:
2962:
2957:
2952:
2947:
2942:
2937:
2931:
2929:
2925:
2924:
2922:
2921:
2910:
2909:
2897:
2896:
2889:
2888:
2881:
2874:
2866:
2857:
2856:
2854:
2853:
2847:
2845:
2841:
2840:
2838:
2837:
2831:
2829:
2825:
2824:
2821:
2820:
2818:
2817:
2810:
2808:
2802:
2801:
2799:
2798:
2791:
2789:
2783:
2782:
2780:
2779:
2776:Caucher Birkar
2773:
2766:
2764:
2755:
2751:
2750:
2743:
2741:
2738:
2737:
2735:
2734:
2729:
2727:Hossein Zakeri
2724:
2719:
2714:
2709:
2704:
2699:
2694:
2684:
2679:
2664:Lotfi A. Zadeh
2661:
2656:
2651:
2646:
2636:
2634:Siamak Yassemi
2631:
2621:
2611:
2606:
2604:Caucher Birkar
2601:
2595:
2593:
2589:
2588:
2586:
2585:
2580:
2575:
2570:
2560:
2555:
2550:
2545:
2543:Kushyar Gilani
2540:
2535:
2530:
2525:
2520:
2502:
2492:
2486:
2484:
2475:
2473:Mathematicians
2469:
2468:
2463:
2462:
2455:
2448:
2440:
2434:
2433:
2417:
2401:
2385:
2369:
2364:
2359:
2354:
2336:(2): 225–262.
2325:
2314:
2295:
2294:External links
2292:
2291:
2290:
2268:
2257:10.1086/349363
2238:
2227:10.2307/595221
2208:
2189:10.1086/349146
2183:(2): 180–183,
2170:
2159:10.1086/348036
2153:(1–2): 56–59,
2135:
2132:
2131:
2130:
2120:
2117:
2115:
2114:
2069:
2054:
2032:
1987:
1972:
1957:
1940:
1923:
1910:
1897:
1874:
1860:
1856:
1852:
1848:
1844:
1840:
1818:
1815:
1789:
1786:
1761:
1758:
1754:
1750:
1745:
1742:
1738:
1734:
1731:
1728:
1723:
1719:
1714:
1710:
1684:
1681:
1659:
1656:
1653:
1625:
1621:
1616:
1612:
1609:
1606:
1603:
1598:
1595:
1592:
1588:
1583:
1579:
1576:
1571:
1568:
1565:
1561:
1556:
1552:
1526:
1509:
1497:
1491:
1469:
1439:
1405:
1398:
1378:
1365:
1352:
1336:
1323:
1310:
1275:
1266:
1240:
1228:Scientific Lib
1215:
1205:
1187:
1177:
1159:
1146:
1120:
1072:
1070:
1067:
1044:
1041:
987:
984:
933:In discussing
930:
927:
859:
853:
851:
846:
832:
829:
824:
820:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
773:François Viète
758:western Europe
741:
738:
735:
732:
727:
723:
671:
666:
644:law of cosines
635:
634:Law of cosines
632:
630:
627:
582:
579:
562:
559:
517:armillary and
498:
493:
475:, such as the
469:Sullam al-Sama
464:
459:
374:
369:
367:
364:
282:
279:
220:
219:
217:
216:
207:
206:
205:
202:
201:
197:
196:
185:
181:
180:
178:Sullam al-Sama
175:
171:
170:
168:Law of cosines
160:
156:
155:
146:
142:
141:
136:
132:
131:
122:
118:
117:
112:
108:
107:
98:
96:(aged 48)
86:
82:
81:
72:
63:
59:
58:
54:
53:
50:
46:
45:
34:
26:
25:
22:
15:
9:
6:
4:
3:
2:
5206:
5195:
5192:
5190:
5187:
5185:
5182:
5180:
5177:
5175:
5172:
5170:
5167:
5165:
5162:
5160:
5157:
5155:
5152:
5150:
5147:
5146:
5144:
5129:
5126:
5124:
5121:
5119:
5116:
5113:
5109:
5105:
5102:
5100:
5097:
5096:
5094:
5090:
5084:
5081:
5079:
5076:
5074:
5071:
5070:
5068:
5064:
5058:
5055:
5053:
5050:
5048:
5045:
5044:
5042:
5038:
5032:
5029:
5027:
5024:
5022:
5019:
5017:
5014:
5012:
5009:
5007:
5004:
5002:
4999:
4997:
4994:
4993:
4991:
4987:
4981:
4978:
4976:
4973:
4972:
4970:
4966:
4960:
4959:
4955:
4953:
4952:
4948:
4946:
4945:
4941:
4939:
4938:
4934:
4932:
4931:
4927:
4925:
4924:
4920:
4918:
4917:
4913:
4911:
4910:
4906:
4904:
4903:
4899:
4897:
4896:
4892:
4891:
4889:
4887:
4881:
4876:
4862:
4859:
4857:
4854:
4852:
4849:
4847:
4844:
4843:
4841:
4837:
4831:
4828:
4826:
4823:
4821:
4818:
4816:
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4787:
4785:
4781:
4775:
4772:
4770:
4767:
4765:
4762:
4760:
4759:Ibn al-Shatir
4757:
4755:
4752:
4751:
4749:
4745:
4739:
4736:
4734:
4733:Ibn al-Banna'
4731:
4729:
4726:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4686:
4684:
4681:
4679:
4678:Ahmad al-Buni
4676:
4674:
4671:
4670:
4668:
4664:
4658:
4655:
4653:
4650:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4624:
4622:
4618:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4592:
4589:
4587:
4584:
4582:
4579:
4577:
4574:
4572:
4569:
4567:
4564:
4562:
4559:
4557:
4554:
4552:
4549:
4547:
4544:
4543:
4541:
4537:
4531:
4528:
4526:
4523:
4521:
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4501:
4498:
4496:
4493:
4491:
4488:
4486:
4483:
4481:
4478:
4476:
4473:
4471:
4468:
4466:
4463:
4461:
4458:
4456:
4453:
4451:
4448:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4407:
4405:
4401:
4395:
4392:
4390:
4387:
4385:
4382:
4380:
4377:
4375:
4372:
4370:
4367:
4365:
4362:
4360:
4357:
4355:
4352:
4350:
4347:
4345:
4342:
4340:
4337:
4335:
4332:
4330:
4327:
4325:
4322:
4320:
4319:Sanad ibn Ali
4317:
4315:
4312:
4311:
4309:
4305:
4302:
4300:
4296:
4292:
4285:
4280:
4278:
4273:
4271:
4266:
4265:
4262:
4242:
4239:
4237:
4234:
4232:
4229:
4227:
4224:
4223:
4221:
4217:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4192:
4190:
4186:
4177:
4173:
4170:
4166:
4163:
4159:
4158:
4157:
4156:Observatories
4154:
4152:
4149:
4147:
4144:
4142:
4139:
4137:
4134:
4133:
4131:
4127:
4121:
4118:
4116:
4113:
4111:
4110:Triangulation
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4020:Heliocentrism
4018:
4016:
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3922:
3920:
3916:
3910:
3907:
3905:
3902:
3900:
3897:
3895:
3894:Shadow square
3892:
3890:
3887:
3885:
3882:
3880:
3877:
3875:
3872:
3870:
3867:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3845:
3842:
3840:
3837:
3835:
3832:
3830:
3827:
3825:
3822:
3820:
3817:
3815:
3812:
3810:
3807:
3805:
3802:
3800:
3797:
3795:
3792:
3791:
3789:
3787:
3783:
3773:
3772:
3768:
3766:
3765:
3764:Zij-i Sultani
3761:
3759:
3758:
3757:Zij-i Ilkhani
3754:
3752:
3749:
3747:
3746:
3742:
3740:
3739:
3735:
3733:
3730:
3729:
3727:
3725:
3724:
3719:
3713:
3712:
3708:
3706:
3705:
3701:
3699:
3698:
3694:
3692:
3691:
3687:
3685:
3684:
3680:
3678:
3675:
3673:
3670:
3669:
3666:
3663:
3659:
3655:
3648:
3644:
3630:
3627:
3625:
3622:
3620:
3617:
3615:
3612:
3611:
3609:
3605:
3599:
3596:
3594:
3591:
3589:
3586:
3584:
3581:
3579:
3576:
3575:
3573:
3569:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3543:
3540:
3538:
3535:
3533:
3532:Kadızade Rumi
3530:
3528:
3525:
3523:
3520:
3518:
3515:
3514:
3512:
3508:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3456:Ibn al-Shatir
3454:
3453:
3451:
3447:
3441:
3438:
3436:
3433:
3431:
3430:Ibn al‐Raqqam
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3352:
3350:
3346:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3324:Ibn al-Kammad
3322:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3281:
3279:
3275:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3251:
3249:
3246:
3244:
3241:
3239:
3238:Ibn al-Saffar
3236:
3234:
3231:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3206:
3204:
3201:
3200:
3198:
3194:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3158:
3155:
3153:
3150:
3148:
3145:
3143:
3140:
3138:
3135:
3133:
3130:
3128:
3125:
3123:
3120:
3118:
3115:
3113:
3110:
3108:
3105:
3103:
3100:
3098:
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3073:
3070:
3069:
3067:
3063:
3057:
3054:
3052:
3049:
3047:
3044:
3042:
3039:
3037:
3034:
3032:
3029:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2973:
2971:
2967:
2961:
2958:
2956:
2953:
2951:
2948:
2946:
2943:
2941:
2938:
2936:
2933:
2932:
2930:
2926:
2919:
2918:
2915:
2911:
2907:
2902:
2898:
2894:
2887:
2882:
2880:
2875:
2873:
2868:
2867:
2864:
2852:
2849:
2848:
2846:
2842:
2836:
2833:
2832:
2830:
2828:Organizations
2826:
2815:
2812:
2811:
2809:
2807:
2803:
2796:
2793:
2792:
2790:
2788:
2784:
2777:
2774:
2771:
2768:
2767:
2765:
2763:
2759:
2756:
2752:
2747:
2733:
2730:
2728:
2725:
2723:
2720:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2692:
2688:
2687:Reza Sarhangi
2685:
2683:
2680:
2677:
2673:
2669:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2644:
2640:
2637:
2635:
2632:
2629:
2625:
2622:
2619:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2596:
2594:
2590:
2584:
2581:
2579:
2576:
2574:
2571:
2568:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2524:
2521:
2518:
2514:
2510:
2506:
2503:
2500:
2496:
2493:
2491:
2488:
2487:
2485:
2479:
2476:
2474:
2470:
2461:
2456:
2454:
2449:
2447:
2442:
2441:
2438:
2430:
2423:
2418:
2414:
2407:
2402:
2398:
2391:
2386:
2382:
2375:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2351:
2347:
2343:
2339:
2335:
2331:
2326:
2323:
2317:
2311:
2307:
2303:
2298:
2297:
2288:
2284:
2283:
2278:
2274:
2269:
2266:
2262:
2258:
2254:
2250:
2246:
2245:
2239:
2236:
2232:
2228:
2224:
2220:
2216:
2215:
2209:
2206:
2202:
2198:
2194:
2190:
2186:
2182:
2178:
2177:
2171:
2168:
2164:
2160:
2156:
2152:
2148:
2147:
2142:
2138:
2137:
2129:
2123:
2122:
2109:
2103:
2089:on 2011-07-22
2088:
2084:
2079:
2073:
2066:
2063:
2058:
2051:
2047:
2044:
2041:
2036:
2029:
2026:, and of the
2025:
2021:
2017:
2013:
2009:
2005:
2001:
1997:
1991:
1984:
1981:
1976:
1969:
1966:
1961:
1954:
1950:
1944:
1937:
1933:
1927:
1920:
1914:
1907:
1901:
1895:
1894:0-691-02397-2
1891:
1887:
1884:D.J. Struik,
1881:
1879:
1858:
1854:
1850:
1846:
1842:
1838:
1816:
1813:
1804:
1787:
1784:
1759:
1756:
1752:
1748:
1743:
1740:
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1729:
1726:
1721:
1717:
1712:
1708:
1699:
1682:
1679:
1657:
1654:
1651:
1643:system. With
1642:
1623:
1619:
1614:
1610:
1607:
1604:
1601:
1596:
1593:
1590:
1586:
1581:
1577:
1574:
1569:
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1563:
1559:
1554:
1550:
1541:
1524:
1513:
1506:
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1492:0-88385-546-1
1488:
1484:
1480:
1473:
1466:
1462:
1458:
1454:
1450:
1443:
1435:
1431:
1427:
1423:
1416:
1409:
1401:
1399:9781402757969
1395:
1391:
1390:
1382:
1375:
1369:
1362:
1356:
1349:
1343:
1341:
1334:, p. 56)
1333:
1327:
1320:
1314:
1307:
1303:
1302:
1297:
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1255:
1251:
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1150:
1143:
1142:
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1129:
1124:
1116:
1110:
1095:
1091:
1090:Maths History
1087:
1080:
1078:
1073:
1066:
1064:
1060:
1056:
1055:
1050:
1039:
1037:
1033:
1029:
1025:
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1017:
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1009:
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910:Kerala School
907:
903:
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899:
895:
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830:
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818:
814:
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793:
790:
787:
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767:
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733:
730:
725:
721:
712:
708:
703:
701:
697:
693:
689:
685:
677:
670:
665:
663:
659:
655:
654:triangulation
651:
650:
645:
641:
626:
624:
620:
616:
612:
608:
604:
600:
596:
592:
588:
578:
576:
572:
568:
558:
556:
552:
548:
544:
540:
536:
532:
528:
524:
521:armillary of
520:
516:
512:
508:
504:
497:
492:
490:
486:
482:
478:
474:
470:
463:
458:
456:
452:
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444:
440:
436:
432:
428:
424:
420:
416:
412:
408:
404:
400:
396:
395:
394:Zij-i Ilkhani
390:
386:
383:entitled the
382:
381:
373:
363:
359:
357:
353:
349:
345:
340:
338:
334:
330:
325:
323:
319:
315:
308:
303:
296:
292:
287:
278:
276:
271:
269:
265:
264:mathematician
261:
257:
253:
249:
245:
241:
234:
230:
226:
215:
212:
211:
203:
200:Muslim leader
198:
195:
192:
189:
186:
182:
179:
176:
172:
169:
164:
161:
157:
154:
150:
147:
143:
140:
137:
133:
130:
126:
123:
119:
116:
113:
109:
105:
101:
87:
83:
79:
75:
64:
60:
55:
51:
47:
42:
38:
32:
27:
20:
4956:
4949:
4942:
4935:
4928:
4921:
4914:
4907:
4900:
4893:
4884:Mathematical
4839:16th century
4799:
4790:Ibn al-Majdi
4783:15th century
4747:14th century
4666:13th century
4620:12th century
4606:Omar Khayyam
4539:11th century
4435:Aṣ-Ṣaidanānī
4403:10th century
4364:Al-Khwarizmi
4129:Institutions
3980:Eccentricity
3940:Astrophysics
3834:Compass rose
3769:
3762:
3755:
3743:
3736:
3721:
3709:
3702:
3695:
3688:
3681:
3547:Ibn al-Majdi
3526:
3522:Abd al‐Wajid
3481:Al-Wabkanawi
3476:Abū al‐ʿUqūl
3365:Jamal ad-Din
3334:Omar Khayyam
3162:Al-ʻIjliyyah
3137:Aṣ-Ṣaidanānī
3122:Ibn al-A'lam
3041:Al-Khwarizmi
2844:Institutions
2806:Satter Prize
2762:Fields Medal
2712:Reza Sadeghi
2624:S. L. Hakimi
2563:Al-Khwarizmi
2505:Omar Khayyam
2494:
2483:20th Century
2428:
2412:
2396:
2380:
2333:
2329:
2305:
2280:
2251:(1): 42–50,
2248:
2242:
2218:
2212:
2180:
2174:
2150:
2144:
2091:. Retrieved
2087:the original
2077:
2072:
2061:
2057:
2039:
2035:
2011:
2003:
1995:
1990:
1979:
1975:
1964:
1960:
1952:
1948:
1943:
1935:
1931:
1926:
1918:
1917:J. Needham,
1913:
1905:
1900:
1885:
1697:
1539:
1512:
1504:
1500:
1478:
1472:
1456:
1452:
1442:
1425:
1421:
1408:
1388:
1381:
1374:Kennedy 1951
1368:
1361:Kennedy 1952
1355:
1348:Kennedy 1950
1332:Kennedy 1947
1326:
1319:Kennedy 1951
1313:
1299:
1269:
1257:. Retrieved
1253:
1243:
1231:. Retrieved
1227:
1218:
1210:
1196:
1190:
1182:
1168:
1162:
1155:
1149:
1139:
1123:
1097:. Retrieved
1089:
1058:
1052:
1046:
1019:
1008:Song dynasty
1001:
996:Omar Khayyám
989:
978:
963:Simon Stevin
958:
950:
944:
932:
913:
861:
848:
777:
770:
765:
762:Henry Briggs
753:
704:
698:for solving
675:
673:
668:
661:
657:
647:
637:
605:in terms of
584:
564:
502:
500:
495:
466:
461:
398:
392:
384:
378:
376:
371:
360:
341:
326:
311:
306:
295:Safavid Iran
290:
272:
239:
228:
224:
223:
88:22 June 1429
43:, dated 1656
41:Safavid Iran
36:
5154:1429 deaths
5149:1380 births
4902:De Gradibus
4856:Taqi ad-Din
4846:Al-Birjandi
4820:al-Qalaṣādī
4601:Al-Isfizari
4566:Ibn al-Samh
4495:Al-Isfahani
4475:al-Uqlidisi
4445:al-Khojandi
4410:Abu al-Wafa
4349:al-Dinawari
4307:9th century
4115:Tusi couple
4105:Trepidation
4070:Salah times
4005:Geocentrism
3879:Planisphere
3859:Graph paper
3786:Instruments
3738:Huihui Lifa
3619:Ehmedê Xanî
3578:Al-Birjandi
3557:al-Kubunani
3314:Abu al-Salt
3263:Al-Isfizari
3223:Ibn al-Samh
3102:Abu al-Wafa
3087:al-Khojandi
2991:Al-Farghani
2906:Astronomers
2795:Sara Zahedi
2676:Fuzzy logic
2609:Sara Zahedi
2558:Al-Isfizari
2553:Al-Isfahani
2322:PDF version
1934:, footnote
1904:P. Luckey,
1453:SIAM Review
1259:14 November
1233:14 November
1099:14 November
1032:Peter Apian
1024:Renaissance
975:sexagesimal
967:Netherlands
898:Zu Chongzhi
892:, AD 150),
874:sexagesimal
684:Taqi al-Din
629:Mathematics
539:al-Khujandi
515:equinoctial
435:sexagesimal
411:observatory
399:Khaqani Zij
391:'s earlier
385:Khaqani Zij
372:Khaqani Zij
356:Middle East
352:Middle East
256:Transoxania
242:) (c. 1380
153:Mathematics
104:Transoxania
69: 1380
5143:Categories
5066:Influenced
5040:Influences
4810:Ali Qushji
4769:Al-Khalili
4637:Al-Khazini
4632:Al-Kharaqī
4591:al-Zarqālī
4581:al-Jayyānī
4525:al-Majriti
4510:Abu al-Jud
4480:Al-Battani
4455:Al-Saghani
4450:Al-Nayrizi
4389:al-Marwazi
4324:al-Jawharī
4219:Influenced
4188:Influences
4060:Precession
4040:Multiverse
3945:Axial tilt
3925:Almucantar
3909:Triquetrum
3849:Equatorium
3598:Takiyüddin
3471:al-Battiwi
3466:Ibn Shuayb
3461:Al-Khalili
3304:Al-Khazini
3299:Al-Kharaqī
3294:Ibn Tufail
3284:Al-Bitruji
3218:Al-Zarqālī
3182:al-Majriti
3132:Al-Saghani
3127:Al-Nayrizi
3112:al-Battani
3031:Iranshahri
3016:Al-Marwazi
2920:by century
2538:Al-Nayrizi
2134:References
2093:2009-10-04
1700:less than
1540:inaccuracy
1250:"al-Kāshī"
1178:9004057455
951:De Thiende
601:, and the
519:solsticial
507:triquetrum
487:, and the
419:university
417:) and his
260:astronomer
229:al-Kāshānī
214:Ali Qushji
208:Influenced
184:Occupation
92:1429-06-23
4815:al-Wafa'i
4805:Ulugh Beg
4708:al-Abhari
4693:Ibn Adlan
4683:Ibn Munim
4647:al-Hassar
4586:al-Nasawī
4561:Al-Biruni
4530:al-Jabali
4520:Al-Karaji
4470:Ibn Yunus
4425:Abu Kamil
4420:Al-Qabisi
4415:al-Khazin
4344:Al-Mahani
4095:Supernova
4050:Obliquity
4035:Moonlight
3935:Astrology
3814:Astrolabe
3593:Piri Reis
3583:al-Khafri
3552:al-Wafa'i
3537:Ulugh Beg
3517:Ali Kuşçu
3491:al-Jadiri
3410:al-Abhari
3208:al-Biruni
3142:Ibn Yunus
3117:Al-Qabisi
3092:al-Khazin
3001:Al-Mahani
2787:EMS Prize
2672:Fuzzy set
2583:Al-Biruni
2523:Al-Mahani
2350:248336832
2265:123582209
2167:143993402
1994:The name
1955:(Girard).
1817:π
1788:π
1757:−
1741:−
1733:×
1727:≈
1683:π
1605:⋯
1047:In 2009,
949:pamphlet
831:ϕ
828:
812:−
809:ϕ
806:
794:ϕ
788:
731:−
662:muhītīyya
658:Risāla al
646:is named
611:latitudes
591:longitude
543:Samarqand
407:Ulugh Beg
397:. In his
366:Astronomy
348:Samarkand
344:Ulugh Beg
333:Goharshad
329:Shah Rokh
322:Tamerlane
281:Biography
268:Tamerlane
258:) was an
252:Samarkand
149:Astronomy
100:Samarkand
4968:Concepts
4800:al-Kāshī
4774:al-Umawi
4576:Avicenna
4515:Al-Sijzi
4465:Ibn Sahl
4334:Al-Kindi
4169:Maragheh
4120:Universe
4090:Sunlight
4055:Parallax
4045:Muwaqqit
3985:Ecliptic
3918:Concepts
3884:Quadrant
3804:Aperture
3319:Averroes
3289:Avempace
3233:Avicenna
3167:Nastulus
3157:al-Sijzi
3082:Al-Adami
2996:Al-Kindi
2205:43217299
2197:15436217
2119:See also
2102:cite web
2046:Archived
1505:Al-Kashi
1109:cite web
1004:Yang Hui
959:La Disme
619:alhidade
615:ecliptic
587:computer
555:alhidade
551:altitude
427:theology
423:Madrasah
337:sciences
111:Religion
57:Personal
52:al-Kashi
5092:Related
5021:Madrasa
4989:Centers
4795:al-Rūmī
4698:al-Urdi
4596:ibn Hud
4551:Alhazen
4505:al-Qūhī
4025:Inertia
4015:Gravity
3950:Azimuth
3899:Sundial
3889:Sextant
3839:Dioptra
3829:Compass
3794:Alidade
3405:al-Urdi
3228:Alhazen
3152:Ma Yize
3097:al-Qūhī
3072:al-Sufi
2567:Al-jabr
2481:Before
2000:Persian
1947:Smith,
1641:decimal
1639:in the
971:Chinese
947:Flemish
906:Madhava
890:Ptolemy
882:decimal
862:In his
764:in his
688:algebra
603:planets
593:of the
547:Azimuth
535:sextant
531:versine
453:to the
445:on the
439:decimal
403:Timurid
318:Persian
233:Persian
194:scholar
188:Persian
90: (
4000:Galaxy
3995:Equant
3930:Apogee
3874:Octant
3651:Topics
2816:(2013)
2797:(2016)
2778:(2018)
2772:(2014)
2592:Modern
2348:
2312:
2263:
2235:595221
2233:
2203:
2195:
2165:
2022:, the
2018:, the
2008:Arabic
1892:
1805:. For
1489:
1396:
1203:
1175:
1036:German
1028:Pascal
955:Leyden
939:Struik
880:to 16
642:, the
640:French
609:; the
525:, the
513:, the
483:, the
479:, the
314:Kashan
275:Europe
244:Kashan
191:Muslim
135:Region
74:Kashan
4886:works
4065:Qibla
3854:Globe
3661:Works
2425:(PDF)
2409:(PDF)
2393:(PDF)
2377:(PDF)
2346:S2CID
2261:S2CID
2231:JSTOR
2201:S2CID
2163:S2CID
2028:stars
2016:Earth
1839:6.283
1698:error
1428:(1).
1418:(PDF)
1069:Notes
1012:China
872:to 9
756:. In
623:ruler
489:Stars
477:Earth
421:(see
413:(see
115:Islam
49:Title
3607:17th
3571:16th
3510:15th
3449:14th
3348:13th
3277:12th
3196:11th
3065:10th
2310:ISBN
2244:Isis
2193:PMID
2176:Isis
2146:Isis
2108:link
2024:Moon
1953:II.9
1890:ISBN
1749:<
1730:9.92
1487:ISBN
1394:ISBN
1261:2023
1235:2023
1201:ISBN
1173:ISBN
1130:and
1115:link
1101:2023
1049:IRIB
690:and
621:and
599:Moon
597:and
529:and
527:sine
509:and
481:Moon
431:sine
262:and
248:Iran
227:(or
139:Iran
85:Died
78:Iran
62:Born
4958:Zij
3723:Zij
3077:Ibn
2969:9th
2928:8th
2338:doi
2253:doi
2223:doi
2185:doi
2155:doi
2020:Sun
1932:I.3
1859:476
1855:586
1851:179
1847:307
1843:185
1461:doi
1430:doi
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1010:in
908:of
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674:In
638:In
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537:of
485:Sun
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740:0
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726:P
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
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