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Al-Tusi was born in Tus, which attempt close to Meshed in north Iran high up in nobility valley of the Kashaf Flood. He was born at justness beginning of a century which would see conquests across grandeur whole of the Islamic sphere from close to China get the east to Europe providential the west. It was nobility era when the vast belligerent power of the Mongols would sweep across the vast areas of the Islamic world displaying a bitter animosity towards Mohammedanism and cruelly massacring people.

That was a period in which there would be little intact and tranquillity for great scholars to pursue their works, bear al-Tusi was inevitably drawn do the conflict engulfing his power.

In Tus, al-Tusi's pop was a jurist in righteousness Twelfth Imam School. The Duodecimal Imam was the main turn the spotlight on of Shi'ite Muslims and birth school where al-Tusi was ormed was mainly a religious formation.

However, while studying in Momentum, al-Tusi was taught other topics by his uncle which would have an important influence archetypal his intellectual development. These topics included logic, physics and knowledge while he also studied add-on other teachers learning mathematics, draw particular algebra and geometry.

In 1214, when al-Tusi was 13 years old, Genghis Caravansary, who was the leader work out the Mongols, turned away carry too far his conquests in China wallet began his rapid advance en route for the west. It would put together be too long before al-Tusi would see the effects pointer these conquests on his fall on regions, but before that exemplification he was able to lucubrate more advanced topics.

From Energy, al-Tusi went to Nishapur which is 75 km west hint at Tus. Nishapur was a good choice for al-Tusi to finished his education since it was an important centre of exhibition. There al-Tusi studied philosophy, rebuke and mathematics. In particular soil was taught mathematics by Kamal al-Din ibn Yunus, who herself had been a pupil only remaining Sharaf al-Din al-Tusi.

While score Nishapur al-Tusi began to make fast a reputation as an incomplete scholar and became well systematic throughout the area.

Say publicly Mongol invasion reached the proposal of Tus around 1220 present-day there was much destruction. Genghis Khan turned his attention take up again towards the east leaving sovereign generals and sons in justness west to continue his conquests.

There was, amid the common fighting in the region, compassionate havens which attracted al-Tusi. Picture Assassins, who practised an man of letters form of extremist Shi'ism, harnessed the castle of Alamut hem in the Elburz Mountains, and curb similar impregnable forts in depiction mountains. When invited by prestige Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim to join the find ways to help of the Assassins, al-Tusi nose-dive and became a highly believed member of the Isma'ili Retinue.

Whether he would have antique able to leave, had take action wished to, is not altogether clear. However, al-Tusi did callous of his best work linctus moving round the different strongholds, and during this period explicit wrote important works on deduction, philosophy, mathematics and astronomy. Class first of these works, Akhlaq-i nasiri, was written in 1232.

It was a work mandate ethics which al-Tusi dedicated attain the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim.

In 1256 al-Tusi was in the fastness of Alamut when it was attacked by the forces foothold the Mongol leader Hulegu, capital grandson of Genghis Khan, who was at that time avid on extending Mongol power slot in Islamic areas.

Some claim make certain al-Tusi betrayed the defences be advantageous to Alamut to the invading Mongols. Certainly Hulegu's forces destroyed Alamut and, Hulegu himself being living soul interested in science, he prearranged al-Tusi with great respect. Curtail may be that indeed al-Tusi felt that he was be the source of held in Alamut against emperor will, for certainly he seemed enthusiastic in joining the unvanquished Mongols who appointed him little their scientific advisor.

He was also put in charge describe religious affairs and was confront the Mongol forces under Hulegu when they attacked Baghdad well-heeled 1258.

Al-Musta'sim, the mug Abbasid caliph in Baghdad, was a weak leader and blooper proved no match for Hulegu's Mongol forces when they played Baghdad. After having laid lay siege to to the city, the Mongols entered it in February 1258 and al-Musta'sim together with Ccc of his officials were murdered.

Hulegu had little sympathy be smitten by a city after his make a hit had won a battle, unexceptional he burned and plundered greatness city and killed many get a hold its inhabitants. Certainly al-Tusi locked away made the right move reorganization far as his own refuge was concerned, and he would also profit scientifically by wreath change of allegiance.

Hulegu was very pleased with rulership conquest of Baghdad and likewise pleased that such an cap scholar as al-Tusi had spliced him. So, when al-Tusi tingle Hulegu with plans for decency construction of a fine Lookout, Hulegu was happy to comply. Hulegu had made Maragheh surmount capital . Maragheh was slot in the Azerbaijan region of northwest Iran, and it was withdraw Maragheh that the Observatory was to be built.

Construction stare the Observatory began in 1259 west of Maragheh, and be there of it can still endure seen there today.

Goodness observatory at Maragheh became operable in 1262. Interestingly the Persians were assisted by Chinese astronomers in the construction and aid of the observatory. It challenging various instruments such as exceptional 4 metre wall quadrant uncomplicated from copper and an angle quadrant which was the devising of Al-Tusi himself.

Al-Tusi as well designed other instruments for blue blood the gentry Observatory which was far very than a centre for physics. It possessed a fine writing-room with books on a ample range of scientific topics, time work on science, mathematics enthralled philosophy were vigorously pursued in the matter of.

Al-Tusi put his Construction to good use, making exceedingly accurate tables of planetary movements.

He published Zij-i ilkhani(the Ilkhanic Tables), written first in Farsi and later translated into Semitic, after making observations for 12 years. This work contains tables for computing the positions more than a few the planets, and it extremely contains a star catalogue. That was not the only mark off work which al-Tusi produced intimate astronomy.

It is fair house say that al-Tusi made decency most significant development of Ptolemy's model of the planetary pathway up to the development run through the heliocentric model in loftiness time of Copernicus. In al-Tusi's major astronomical treatise, al-Tadhkira fi'ilm al-hay'a(Memoir on astronomy) he [17]:-

...

devised a new replica of lunar motion, essentially dissimilar from Ptolemy's. Abolishing the anomalous and the centre of prosneusis, he founded it exclusively joint the principle of eight everywhere rotating spheres and thereby succeeded in representing the irregularities holiday lunar motion with the selfsame exactness as the "Almagest" Ⓣ.

His claim that the extreme difference in longitude between blue blood the gentry two theories amounts to 10 proves perfectly true. In top model Nasir, for the labour time in the history accuse astronomy, employed a theorem falsified by himself which, 250 period later, occurred again in Astronomer, "De Revolutionibus", III 4.

The aim of al-Tusi with this result was let your hair down remove all parts of Ptolemy's system that were not home-grown on the principle of homogeneous circular motion. Many historians stomach that the Tusi-couple result was used by Copernicus after filth discovered it in Al-Tusi's borer, but not all agree; perceive for example [38] where volatility is claimed that Copernicus took the result from Proclus's Commentary on the first book show Euclid and not from al-Tusi.

Among numerous other endowment to astronomy, al-Tusi calculated excellence value of 51' for decency precession of the equinoxes. Inaccuracy also wrote works on colossal instruments, for example on architecture and using an astrolabe.

In logic al-Tusi followed decency teachings of ibn Sina. Soil wrote five works on leadership subject, the most important past it which is one on removal.

In [33] Street describes that as follows:-

Tusi, a ordinal century logician writing in Semite, uses two logical connectives seat build up molecular propositions: 'if-then', and 'either-or'. By referring acquiesce a dichotomous tree, Tusi shows how to choose the accountable disjunction relative to the conditions in the disjuncts.

He further discusses the disjunctive propositions which follow from a conditional proposition.

In the display work al-Tusi discussed objections not easy by earlier mathematicians to examination lengths of straight lines lecture of curved lines. Al-Tusi argues that comparisons are legitimate, disdain the objections that, being fluctuating entities, they are incomparable.

Ptolemy's AlmagestⓉ was one of birth works which Arabic scientists attacked intently.

In 1247 al-Tusi wrote Tahrir al-Majisti(Commentary on the Almagest) in which he introduced many trigonometrical techniques to calculate tables of sines; see [5] all for details. As in the Zij-i Ilkhahi al-Tusi gave tables insensible sines with entries calculated take delivery of three sexagesimal places for coach half degree of the basis.

One of al-Tusi's greatest important mathematical contributions was loftiness creation of trigonometry as uncomplicated mathematical discipline in its flow right rather than as unbiased a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first existing exposition of the whole practice of plane and spherical trig.

As stated in [1]:-

This work is really the extreme in history on trigonometry despite the fact that an independent branch of bare mathematics and the first cage up which all six cases sales rep a right-angled spherical triangle commerce set forth.

sinAa​=sinBb​=sinCc​.

That work by al-Tusi is virtually certainly not original but degree it is his version admire methods developed by al-Karaji's primary. In the manuscript al-Tusi headstrong the coefficients of the lation of a binomial to unpolished power giving the binomial custom and the Pascal triangle family between binomial coefficients.

Amazement should mention briefly other comedian in which al-Tusi contributed. Sand wrote a famous work contemplate minerals which contains an consequential theory of colour based take into account mixtures of black and milky, and included chapters on wealth apple of one`s e and perfumes. He also wrote on medicine, but his medicinal works are among his smallest important.

Much more important were al-Tusi's contributions to philosophy obtain ethics. In particular in conclusions he asked important questions hunch the nature of space.

Al-Tusi had a number perfect example pupils, one of the unscramble known being Nizam al-a'Raj who also wrote a commentary marking out the AlmagestⓉ.

Another of crown pupils Qutb ad-Din ash-Shirazi gave the first satisfactory mathematical anticipate of the rainbow. Al-Tusi's stress, which continued through these session, is summed up in [1] as follows:-

Al-Tusi's influence, vastly in eastern Islam, was great. Probably, if we take edge your way fields into account, he was more responsible for the awakening of the Islamic sciences amaze any other individual.

His transferral together so many competent scholars and scientists at Maragheh resulted not only in the refreshment of mathematics and astronomy on the contrary also in the renewal tip off Islamic philosophy and even theology.

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2. Biography now Encyclopaedia Britannica.
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   Akad. Nauk Azerbaidzan. SSR Ser. Fiz.-Tehn. Mat. Nauk(4)(1977), 114-121.

6. S A Ahmedov, Extraction confiscate a root of any come off and the binomial formula pin down the work of Nasir ad-Din at-Tusi (Russian), Mat. v Skole(5)(1970), 80-82.
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    Hist. Astronom.26(2)(1995)133-154.

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    Gos. Univ. Ucen. Zap. Ser. Fiz.-Mat. Nauk(2)(1969), 83-86.

15. N G Hairetdinova, On honesty history of Nasir ad-Din at-Tusi 's 'Treatise on the quadrilateral' (Russian), Voprosy Istor. Estestvoznan. uncontrollable Tehn.(1)(54)(1976), 42-43, 97, 107.
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17. W Hartner, Nasir al-Din al-Tusi 's lunar theory, Physis - Riv. Internaz. Storia Sci.11(1-4)(1969), 287-304.
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    SSR Poorer. Fiz.-Tehn. Mat. Nauk 1968(1)(1968), 49-54.

19. F A Kasumhanov, The theory pleasant continuous quantities and the scan of number in the complex of Muhammad Nasir-al-din Tusi (Russian), Trudy Inst. Istor. Estest. Tehn.1(1954), 128-145.
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    Estestvoznan. uncontrollable Tehn. Vyp.2(1969), 23-28.

22. T Lévy, Gersonide, le pseudo-Tusi, et le postulat des parallèles. Les mathématiques anesthetize Hébreu et leurs sources arabes, Arabic Sci. Philos.2(1)(1992), 39-82.
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    Nauk Azerbaijzan. SSR Trudy Inst. Mat. Meh. 2(10)(1963), 147-158.

25. J F Ragep, The two versions of the Tusi couple, prosperous From deferent to equant(New Royalty, 1987), 329-356.
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    Estestvoznan. i Tehn.(1)(42)(1972), 36, 95, 103.

28. B A Rozenfeld, On the accurate works of Nasir al-Din al-Tusi (Russian), Istor.-Mat. Issled.4(1951), 489-512.
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30. G Saliba, The role of description 'Almagest' commentaries in medieval Semitic astronomy : a preliminary look into of Tusi's redaction of Ptolemy's 'Almagest', Arch. Internat. Hist. Sci.37(118)(1987), 3-20.
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32. H Tllasev, Firm mathematical and astronomical manuscripts behove Nasir ad-Din at-Tusi in prestige collection of the Institute explain Oriental Studies of the Faculty of Sciences of the Usbeg SSR (Russian), Izv.

    Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk16(4)(1972), 63-65.

33. T Street, Tusi on Avicenna's inferential connectives, Hist. Philos. Logic16(2)(1995), 257-268.
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36. A U Usamanov, Nasir ad-Din at-Tusi's astronomical tract 'Muiniya' (Russian), patent Mathematics in the East underside the Middle Ages(Tashkent, 1978), 113-126, 195.
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    Hist. Astronom.4(2)(1973), 128-130.

39. B van Dalen, Fix S Kennedy and M Adolescent Saiyid, The Chinese-Uighur calendar pull Tusi's 'Zij-i Ilkhani', Z. Gesch. Arab.-Islam. Wiss.11(1997), 111-152, 9.
40. V Merciless Vladimirov, The great Azerbaijani schoolboy Nasir ad-Din at-Tusi (Russian), Izv.

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41. G Fix Yusupova, Commentaries to Menelaus' 'Spherics' by al-Tusi and al-Yazdi (Russian), Izv. Akad. Nauk UzSSR Sink. Fiz.-Mat. Nauk(6)(1990), 40-43, 80.

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Written by J Particularize O'Connor and E F Robertson
Last Update July 1999