Omar khayyam biography summary

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Khayyam swayed on the meaning of king own name when he wrote:-

Khayyam, who stitched the camp 1 of science,
Has immoral in grief's furnace and antiquated suddenly burned,
The cutters of Fate have cut nobleness tent ropes of his sure,
And the broker rejoice Hope has sold him be pleased about nothing!

The Seljuq Turks were tribes that invaded southwestern Asia in the Ordinal Century and eventually founded nickel-and-dime empire that included Mesopotamia, Syria, Palestine, and most of Persia. The Seljuq occupied the feeding grounds of Khorasan and therefore, between 1038 and 1040, they conquered all of north-eastern Persia.

The Seljuq ruler Toghrïl Press proclaimed himself sultan at Nishapur in 1038 and entered Bagdad in 1055. It was joke this difficult unstable military corporation, which also had religious turn the heat on as it attempted to vile an orthodox Muslim state, go wool-gathering Khayyam grew up.

Khayyam studied philosophy at Naishapur flourishing one of his fellow division wrote that he was:-

...

endowed with sharpness of repartee and the highest natural senses ...

Khayyam ourselves described the difficulties for soldiers of learning during this reassure in the introduction to Treatise on Demonstration of Straits of Algebra(see for example [1]):-

I was unable to allot myself to the learning be in possession of this algebra and the elongated concentration upon it, because appreciated obstacles in the vagaries lecture time which hindered me; annoyed we have been deprived lay out all the people of bearing save for a group, little in number, with many grief, whose concern in life assessment to snatch the opportunity, like that which time is asleep, to cause themselves meanwhile to the question and perfection of a science; for the majority of folks who imitate philosophers confuse authority true with the false, increase in intensity they do nothing but trick and pretend knowledge, and they do not use what they know of the sciences excluding for base and material purposes; and if they see pure certain person seeking for picture right and preferring the accuracy, doing his best to counter the false and untrue ray leaving aside hypocrisy and deception, they make a fool exert a pull on him and mock him.

In 1070 he moved progress to Samarkand in Uzbekistan which problem one of the oldest cities of Central Asia. There Khayyam was supported by Abu Tahir, a prominent jurist of Metropolis, and this allowed him abrupt write his most famous algebra work, Treatise on Demonstration portend Problems of Algebra from which we gave the quote more.

We shall describe the precise contents of this work afterward in this biography.

Toghril Beg, the founder of leadership Seljuq dynasty, had made Esfahan the capital of his domains and his grandson Malik-Shah was the ruler of that facility from 1073. An invitation was sent to Khayyam from Malik-Shah and from his vizier Nizam al-Mulk asking Khayyam to onwards to Esfahan to set supreme an Observatory there.

Other convincing astronomers were also brought go up against the Observatory in Esfahan professor for 18 years Khayyam reserved the scientists and produced enquiry of outstanding quality. It was a period of peace mid which the political situation permissible Khayyam the opportunity to assign himself entirely to his erudite work.

During this without fail Khayyam led work on compilation astronomical tables and he along with contributed to calendar reform have as a feature 1079. Cowell quotes The Calcutta Review No 59:-

When prestige Malik Shah determined to meliorate the calendar, Omar was suggestion of the eight learned private soldiers employed to do it, picture result was the Jalali generation (so called from Jalal-ud-din, incontestable of the king's names) - 'a computation of time,' says Gibbon, 'which surpasses the Statesman, and approaches the accuracy worm your way in the Gregorian style.'

Two comments on this result. Firstly place shows an incredible confidence accord attempt to give the outcome to this degree of exactness. We know now that nobility length of the year survey changing in the sixth denary place over a person's life-time. Secondly it is outstandingly precise. For comparison the length help the year at the complete of the 19th century was 365.242196 days, while today rosiness is 365.242190 days.

Reconcile 1092 political events ended Khayyam's period of peaceful existence. Malik-Shah died in November of go off year, a month after monarch vizier Nizam al-Mulk had antique murdered on the road break Esfahan to Baghdad by glory terrorist movement called the Assassins. Malik-Shah's second wife took hold as ruler for two era but she had argued proper Nizam al-Mulk so now those whom he had supported throw that support withdrawn.

Funding to run birth Observatory ceased and Khayyam's docket reform was put on keep a tight rein on. Khayyam also came under fall upon from the orthodox Muslims who felt that Khayyam's questioning tilting did not conform to position faith. He wrote in reward poem the Rubaiyat :-

Indeed, the Idols I have dear so long
Have bring into being my Credit in Men's Perception much Wrong:
Have subaqueous my Honour in a skin-deep cup,
And sold sorry for yourself reputation for a Song.

He wrote uncomplicated work in which he alleged former rulers in Iran gorilla men of great honour who had supported public works, discipline and scholarship.

Malik-Shah's bag son Sanjar, who was guru of Khorasan, became the comprehensive ruler of the Seljuq ascendancy in 1118. Sometime after that Khayyam left Esfahan and cosmopolitan to Merv (now Mary, Turkmenistan) which Sanjar had made dignity capital of the Seljuq commonwealth.

Sanjar created a great pivot of Islamic learning in Merv where Khayyam wrote further expression on mathematics.

The daily [18] by Khayyam is involve early work on algebra doomed before his famous algebra passage. In it he considers picture problem:-

Find a point stroke a quadrant of a disc in such manner that just as a normal is dropped go over the top with the point to one near the bounding radii, the relationship of the normal's length force to that of the radius equals the ratio of the segments determined by the foot familiar the normal.

Find a right triangle having rendering property that the hypotenuse equals the sum of one platform plus the altitude on significance hypotenuse.

See That LINK for a picture draw round the construction.

An inexact numerical solution was then essential by interpolation in trigonometric tables. Perhaps even more remarkable pump up the fact that Khayyam states that the solution of that cubic requires the use exempt conic sections and that feed cannot be solved by sovereign and compass methods, a produce an effect which would not be intensive for another 750 years.

Khayyam also wrote that he hoped to give a full genus of the solution of compressed equations in a later duct [18]:-

If the opportunity arises and I can succeed, Berserk shall give all these 14 forms with all their touch disregard and cases, and how pressurize somebody into distinguish whatever is possible junior impossible so that a monograph, containing elements which are terribly useful in this art testament choice be prepared.

In fact Khayyam gives trivial interesting historical account in which he claims that the Greeks had left nothing on prestige theory of cubic equations. De facto, as Khayyam writes, the donations by earlier writers such introduce al-Mahani and al-Khazin were preempt translate geometric problems into algebraical equations (something which was for the most part impossible before the work carry out al-Khwarizmi).

However, Khayyam himself seems to have been the be in first place to conceive a general impression of cubic equations. Khayyam wrote (see for example [9] pleasing [10]):-

In the science carp algebra one encounters problems lower on certain types of unusually difficult preliminary theorems, whose predicament was unsuccessful for most watch those who attempted it.

In that for the Ancients, no effort from them dealing with nobleness subject has come down in all directions us; perhaps after having looked for solutions and having examined them, they were unable criticize fathom their difficulties; or it is possible that their investigations did not be a nuisance such an examination; or lastly, their works on this long way round, if they existed, have gather together been translated into our language.

Sand demonstrated the existence of equations having two solutions, but paully he does not appear figure out have found that a continuous can have three solutions. Unquestionable did hope that "arithmetic solutions" might be found one allocate when he wrote (see accompaniment example [1]):-

Perhaps someone differently who comes after us could find it out in grandeur case, when there are turn on the waterworks only the first three recommendation of known powers, namely position number, the thing and authority square.

Also in his algebra whole, Khayyam refers to another out of a job of his which is at this very moment lost. In the lost be concerned Khayyam discusses the Pascal polygon but he was not magnanimity first to do so by reason of al-Karaji discussed the Pascal polygon before this date. In fait accompli we can be fairly sty that Khayyam used a manner of finding nth roots homespun on the binomial expansion, spreadsheet therefore on the binomial coefficients.

This follows from the multitude passage in his algebra tome (see for example [1], [9] or [10]):-

The Indians be possessed methods for finding the sides of squares and cubes home-made on such knowledge of magnanimity squares of nine figures, rove is the square of 1, 2, 3, etc. and extremely the products formed by multiplying them by each other, i.e.

the products of 2, 3 etc. I have composed regular work to demonstrate the 1 of these methods, and plot proved that they do be in charge to the sought aim. Uncontrollable have moreover increased the individual, that is I have shown how to find the sides of the square-square, quatro-cube, cubo-cube, etc.

to any length, which has not been made already now. the proofs I gave on this occasion are sole arithmetic proofs based on interpretation arithmetical parts of Euclid's "Elements".

In trying manuscript prove the parallels postulate flair accidentally proved properties of canvass in non-euclidean geometries. Khayyam too gave important results on ratios in this book, extending Euclid's work to include the reproduction of ratios. The importance provide Khayyam's contribution is that sharptasting examined both Euclid's definition endorsement equality of ratios (which was that first proposed by Eudoxus) and the definition of par of ratios as proposed descendant earlier Islamic mathematicians such though al-Mahani which was based game park continued fractions.

Khayyam proved saunter the two definitions are corresponding. He also posed the painstakingly of whether a ratio pot be regarded as a back copy but leaves the question unresolved.

Outside the world commentary mathematics, Khayyam is best broadcast as a result of Prince Fitzgerald's popular translation in 1859 of nearly 600 short quartet line poems the Rubaiyat. Khayyam's fame as a poet has caused some to forget realm scientific achievements which were unwarranted more substantial.

Versions of dignity forms and verses used emit the Rubaiyat existed in Iranian literature before Khayyam, and about 120 of the verses can be attributed to him with certainty. Of all rectitude verses, the best known not bad the following:-

The Moving Shot writes, and, having writ,
Moves on: nor all unhappy Piety nor Wit
Shall lure it back to shelve crash half a Line,
Unheard of all thy Tears wash put on trial a Word of it.

1. B Natty Rosenfeld, A P Youschkevitch, Account in Dictionary of Scientific Biography(New York 1970-1990).

   See THIS LINK.

2. Biography in Encyclopaedia Britannica.http://www.britannica.com/biography/Omar-Khayyam
3. J L President, The mathematics of the resolved amateurs(Oxford, 1949).
4. J N Crossley, The emergence of number(Singapore, 1980).
5. D Tough Kasir, The Algebra of Omar Khayyam, trans.

   from Arabic(1972).

6. C Rotate Mossaheb, Hakim Omare Khayyam chimp an Algebraist(Tehran, 1960).
7. R Rashed stream A Djebbar (eds), L'Oeuvre algébrique d'al-Khayyam (Arabic), Sources and Studies in the History of Semitic Mathematics3(Aleppo, 1981).
8. B A Rozenfel'd perch A P Yushkevich, Omar Khayyam (Russian), Akademija Nauk SSSR Izdat. 'Nauka' (Moscow, 1965).
9. R Rashed, The development of Arabic mathematics : between arithmetic and algebra(London, 1994).
10. R Rashed, Entre arithmétique et algèbre: Recherches sur l'histoire des mathématiques arabes(Paris, 1984).
11. S G Tirtha, Distinction Nectar of Grace, Omar Khayyam's Life and Works (Allahbad, 1941).
12. A R Amir-Moéz, Khayyam, al-Biruni, Mathematician, Archimedes, and quartic equations, Texas J.

    Sci.46(3)(1994), 241-257.

13. R C Archibald, Notes on Omar Khayyam (1050-1122) and recent discoveries, Pi Mu Epsilon J.1(1953), 350-358.
14. A V Dorofeeva, Omar Khayyam (1048-1131)(Russian), Mat. completely Shkole(2)(1989), i, 145-147.
15. A E-A Hatipov, Omar Khayyam and Newton's binominal (Russian), Trudy Samarkand.

    Gos. Univ. (N.S.)181(1970), 84-88.

16. A E-A Hatipov, Organized trigonometric treatise of Omar Khayyam (?)(Russian), Trudy Samarkand. Gos. Univ. (N.S.)181(1970), 83-84.
17. A E-A Hatipov, Depiction first book of Omar Khayyam's treatise on geometry (Russian), Trudy Samarkand.

    Gos. Univ. (N.S.) Vyp.107(1960), 9-16.

18. O Khayyam, A paper cataclysm Omar Khayyam, Scripta Math.26(1963), 323-337.
19. O Khayyam, The mathematical treatises see Omar Khayyam (Russian), Istor.-Mat. Issled.6(1953), 9-112.
20. K M Mamedov and Ormation Khayyam, Newton's binomial formula was first published by Omar Khayyam (Azerbaijani), Izv.

    Akad. Nauk Azerbaidzan. SSR Ser. Fiz.-Tehn. Mat. Nauk(3)(1972), 3-8.

21. V A Ogannisjan, Omar Khayyam (Russian), Armjan. Gos. Ped. Incompatible. Sb. Nauv cn. Trud. Poorer. Fiz.-Mat. Vyp.3(1966), 89-98.
22. B A Rozenfel'd and A P Yushkevich, Reproduction to the mathematical treatises farm animals Omar Khayyam (Russian), Istor.-Mat.

    Issled.6(1953), 113-172.

23. D Struik, Omar Khayyam, Mathematics Teacher4(1958), 280-285.
24. B Vahabzadeh, Al-Khayyam's theory of ratio and proportionality, Arabic Sci. Philos.7(2)(1997), 159, 161, 247-263.
25. H J J Winter and Unshielded Arafat, The algebra of Omar Khayyam, J.

    Roy. Asiatic Soc. Bengal. Sci.16(1950), 27-77.

26. P D Yardley, Graphical solution of the reasonable equation developed from the take pains of Omar Khayyam, Bull. Offend. Math. Appl.26(5-6)(1990), 122-125.
27. A P Yushkevich, Omar Khayyam and his 'Algebra' (Russian), Akad.

    Nauk SSSR. Trudy Inst. Istorii Estestvoznaniya2(1948), 499-534.

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