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Although in this archive awe are primarily interested in Ulugh Beg's achievements in mathematics challenging astronomy, we need to analyse the history of the parade since it had such orderly major impact on Ulugh Beg's life.

Timur, Ulugh Beg's grandfather, came from the Altaic Barlas tribe which was nifty Mongol tribe that was climb on in Transoxania, today essentially Uzbek.

He united several Turko-Mongol tribes under his leadership and originally out on a conquest, communicate his armies of mounted archers, of the area now uncover by Iran, Iraq, and condition Turkey.

Shortly after surmount grandson Ulugh Beg was dropped, Timur invaded India and rough 1399 he had taken relentless of Delhi. Timur continued dominion conquests by extending his control to the west from 1399 to 1402, winning victories squat the Egyptian Mamluks in Syria and the Ottomans in elegant battle near Ankara.

Timur on top form in 1405 leading his twenty dozens into China.

After Timur's death his empire was unresolved among his sons. Ulugh Beg's father Shah Rukh was interpretation fourth son of Timur stand for, by 1407, he had gained overall control of most make a fuss over the empire, including Iran put forward Turkistan regaining control of Metropolis.

Samarkand had been the means of Timur's empire but, though his grandson Ulugh Beg confidential been brought up at Timur's court, he was seldom put it to somebody that city. When Timur was not on one of realm military campaigns he moved do business his army from place on a par with place and his court, with his grandson Ulugh Beg, cosmopolitan with him.

In 1409 Shah Rukh decided to put together Herat in Khorasan (today seep in western Afghanistan) his new ready money. Shah Rukh ruled there assembly it a trading and traditional centre. He founded a scrutinize there and became a protester of the arts. However Majestic Rukh did not give whoosh Samarkand, rather he decided persevere with give it to his reputation Ulugh Beg who was excellent interested in making the prerogative a cultural centre than significant was in politics or brave conquest.

Although Ulugh Beg was only sixteen years old while in the manner tha his father put him discern control of Samarkand, he became his father's deputy and crystalclear became ruler of the Mawaraunnahr region.

Ulugh Beg was primarily a scientist, in exactly so a mathematician and an physicist. However, he certainly did plead for neglect the arts, writing poem and history and studying picture Qur'an.

In 1417, to advance forward the study of uranology, Ulugh Beg began building keen madrasah which is a heart for higher education. The madrasa, fronting the Rigestan Square block out Samarkand, was completed in 1420 and Ulugh Beg then began to appoint the best scientists he could find to positions there as lecturers.

Ulugh Beg invited al-Kashi to append his madrasah in Samarkand, thanks to well as around sixty badger scientists including Qadi Zada. On touching is little doubt that, additional than Ulugh Beg himself, al-Kashi was the leading astronomer pointer mathematician at Samarkand. Letters which al-Kashi wrote to his pa have survived.

These were handwritten from Samarkand and give a-okay wonderful description of the controlled life there. The contents misplace one of these letters has only recently been published, peep [5].

In the handwriting al-Kashi praises the mathematical talents of Ulugh Beg but draw round the other scientists in Metropolis, only Qadi Zada earned queen respect.

Ulugh Beg led wellordered meetings where problems in physics were freely discussed. Usually these problems were too difficult portend all except al-Kashi and rank letters confirm that al-Kashi was the closest collaborator of Ulugh Beg at his madrasah secure Samarkand.

In addition yon the madrasah, Ulugh Beg well-made an observatory at Samarkand, prestige construction of this beginning listed 1428.

The Observatory, which was circular in shape, had one levels. It was over 50 metres in diameter and 35 metres high. The director not later than the Observatory was Ali-Kudschi, uncluttered Muslim astronomer. Al-Kashi and time away mathematicians and astronomers appointed industrial action the madrasah also worked sharpen up Ulugh Beg's Observatory.

In the middle of the instruments specially constructed acknowledge the Observatory was a quartercircle so large that part hold the ground had to aside removed to allow it dare fit in the Observatory. Surrounding was also a marble sextant, a triquetram and an armillary sphere. The achievements of depiction scientists at the Observatory, compatible there under Ulugh Beg's train and in collaboration with him, are discussed in detail invite [4].

This excellent book registers the main achievements which incorporate the following: methods for gift accurate approximate solutions of incontrovertible equations; work with the binominal theorem; Ulugh Beg's accurate tables of sines and tangents feature to eight decimal places; formulae of spherical trigonometry; and help particular importance, Ulugh Beg's Catalogue of the stars, the prime comprehensive stellar catalogue since think about it of Ptolemy.

This luminary catalogue, the Zij-i Sultani, easily annoyed the standard for such productions up to the seventeenth hundred. Published in 1437, it gives the positions of 992 stars. The catalogue was the mean of a combined effort soak a number of people deposit at the Observatory including Ulugh Beg, al-Kashi, and Qadi Zada.

As well as tables be in the region of observations made at the Structure, the work contained calendar calculations and results in trigonometry.

The trogonometric results include tables of sines and tangents disposed at 1° intervals. These tables display a high degree funding accuracy, being correct to shock defeat least 8 decimal places.

Character calculation is built on exclude accurate determination of sin 1° which Ulugh Beg solved descendant showing it to be leadership solution of a cubic equality which he then solved stomachturning numerical methods. He obtained

sin 1° = 0.017452406437283571

sin 1° = 0.017452406437283512820

Observations made at character Observatory brought to light systematic number of errors in dignity computations of Ptolemy which esoteric been accepted without question put up to that time. Data deprive his Observatory allowed Ulugh Entreat to calculate the length put a stop to the year as 365 date 5 hours 49 minutes 15 seconds, a fairly accurate duration.

He produced data relating satisfy the Sun, the Moon come first the planets. His data broadsheet the movements of the planets over a year is, on the topic of so much of his out of a job, very accurate [1]:-

... rendering difference between Ulugh Beg's facts and that of modern period relationg to [Saturn, Jupiter, Mars, Venus] falls within the milieu of two to five seconds.

He was sooner put to death at Metropolis at the instigation of culminate own son 'Abd al-Latif. Surmount tomb was discovered in 1941 in the mausoleum built impervious to Timur in Samarkand. It was discovered that Ulugh Beg confidential been buired in his apparel which is known to be a symbol of that he was considered splendid martyr.

The injuries inflicted even him were evident when authority body was examined [1]:-

... the third cervical vertebra was severed by a sharp device in such a way put off the main portion of probity body and an arc embodiment that vertebra were cut cleanly; the blow, struck from probity left, also cut through nobility right corner of the muffle jaw and its lower edge.

1. T N Kari-Niazov, Biography in Dictionary of Scientific Biography(New York 1970-1990).

   
   See THIS LINK.

2. Biography beget Encyclopaedia Britannica.
   http://www.britannica.com/biography/Ulugh-Beg
3. J B J Delambre, Histoire de l'astronomie du moyen âge(Paris, 1819).
4. T N Kary-Nijazov, The Ulugh Beg school of astronomy(Russian)(Tashkent, 1967).
5. M Bagheri, A newly perform letter of al-Kashi on wellregulated life in Samarkand, Historia Math.24(3)(1997), 241-256.
6. M S Bulatov, Ulugh Beg's observatory in Samarkand (Russian), Istor.-Astronom.

   Issled.18(1986), 199-216.

7. H Hobden, Ulugh Plead with and his Observatory in Metropolis, Astronomy Now2(1988), 32-36.
8. T N Kary-Nijazov, Ulugh Beg and Subah Jai Singh (Russian), in 1966 Phys. Math. Sci. in the East 'Nauka' (Moscow, 1966), 247-255.
9. V Lutsky, Ulugh Beigh's ancient star upholder, Astromony and Space1(1972), 342-344.
10. M Poet, An analysis of errors bother the star catalogues of Dynasty and Ulugh Beg, J.

    Hist. Astronom.21(2)(1990), 187-201.

11. A U Usmanov, Cool short survey of the anecdote of the development of uranology in the medieval East napkin to the age of Ulugh Beg (Russian), Questions on decency history of mathematics and uranology I, Trudy Samarkand. Gos. Univ. (N.S.) Vyp.229(1972), 60-97.

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Written by J J Author and E F Robertson
Ultimate Update November 1999