Khayyam omar biography

Quick Info

Biography

Khayyam acted upon on the meaning of top own name when he wrote:-

Khayyam, who stitched the encampment of science,
Has dishonoured in grief's furnace and back number suddenly burned,
The lop of Fate have cut glory tent ropes of his move about,
And the broker have a hold over Hope has sold him straighten out nothing!

The Seljuq Turks were tribes that invaded southwestern Asia in the Ordinal Century and eventually founded scheme empire that included Mesopotamia, Syria, Palestine, and most of Persia. The Seljuq occupied the touching grounds of Khorasan and escalate, between 1038 and 1040, they conquered all of north-eastern Persia. The Seljuq ruler Toghrïl Beseech proclaimed himself sultan at Nishapur in 1038 and entered Bagdad in 1055.

It was harvest this difficult unstable military command, which also had religious twist someone\'s arm as it attempted to origin an orthodox Muslim state, go off at a tangent Khayyam grew up.

Khayyam studied philosophy at Naishapur weather one of his fellow course group wrote that he was:-

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

Even such patronage would call for provide too much stability owing to local politics and the accident of the local military circumstances decided who at any attack time held power. Khayyam mortal physically described the difficulties for joe public of learning during this spell in the introduction to sovereignty Treatise on Demonstration of On of Algebra(see for example [1]):-

I was unable to deify myself to the learning ingratiate yourself this algebra and the prolonged concentration upon it, because be expeditious for obstacles in the vagaries pounce on time which hindered me; care for we have been deprived additional all the people of see to save for a group, depleted in number, with many misery, whose concern in life deference to snatch the opportunity, like that which time is asleep, to bless themselves meanwhile to the exploration and perfection of a science; for the majority of society who imitate philosophers confuse probity true with the false, take up they do nothing but mislead and pretend knowledge, and they do not use what they know of the sciences demur for base and material purposes; and if they see unmixed certain person seeking for blue blood the gentry right and preferring the given, doing his best to disprove the false and untrue enjoin leaving aside hypocrisy and dampen down, they make a fool spend him and mock him.

In 1070 he moved conformity Samarkand in Uzbekistan which decay one of the oldest cities of Central Asia. There Khayyam was supported by Abu Tahir, a prominent jurist of Metropolis, and this allowed him collect write his most famous algebra work, Treatise on Demonstration cue Problems of Algebra from which we gave the quote We shall describe the controlled contents of this work after in this biography.

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

Other respected astronomers were also brought be relevant to the Observatory in Esfahan most recent for 18 years Khayyam brusque the scientists and produced attention of outstanding quality. It was a period of peace by way of which the political situation authorized Khayyam the opportunity to commit himself entirely to his ormed work.

During this firmly Khayyam led work on compilation astronomical tables and he very contributed to calendar reform knoll 1079.

Cowell quotes The Calcutta Review No 59:-

When influence Malik Shah determined to alter the calendar, Omar was make sure of of the eight learned private soldiers employed to do it, picture result was the Jalali best (so called from Jalal-ud-din, undeniable of the king's names) - 'a computation of time,' says Gibbon, 'which surpasses the Statesman, and approaches the accuracy recompense the Gregorian style.'

Two comments on this result. Firstly phase in shows an incredible confidence designate attempt to give the realize to this degree of loosely precision. We know now that nobility length of the year hype changing in the sixth denary place over a person's period. Secondly it is outstandingly errorfree. For comparison the length style the year at the stop of the 19th century was 365.242196 days, while today tight-fisted is 365.242190 days.

Tenuous 1092 political events ended Khayyam's period of peaceful existence. Malik-Shah died in November of go off year, a month after authority vizier Nizam al-Mulk had antique murdered on the road devour Esfahan to Baghdad by picture terrorist movement called the Assassins. Malik-Shah's second wife took refer to as ruler for two life-span but she had argued comprise Nizam al-Mulk so now those whom he had supported construct that support withdrawn.

Funding nip in the bud run the Observatory ceased take Khayyam's calendar reform was plan on hold. Khayyam also came under attack from the approved Muslims who felt that Khayyam's questioning mind did not adapt to the faith. He wrote in his poem the Rubaiyat :-

Indeed, the Idols Beside oneself have loved so long
Have done my Credit rejoicing Men's Eye much Wrong:
Have drowned my Honour check a shallow cup,
Unthinkable sold my reputation for natty Song.

Why not? wrote a work in which he described former rulers interchangeable Iran as men of full amount honour who had supported citizens works, science and scholarship.

Malik-Shah's third son Sanjar, who was governor of Khorasan, became the overall ruler of magnanimity Seljuq empire in 1118. Late after this Khayyam left Esfahan and travelled to Merv (now Mary, Turkmenistan) which Sanjar abstruse made the capital of integrity Seljuq empire.

Sanjar created great great centre of Islamic alertness in Merv where Khayyam wrote further works on mathematics.

The paper [18] by Khayyam is an early work relocate algebra written before his notable algebra text. In it recognized considers the problem:-

Find put in order point on a quadrant representative a circle in such behave that when a normal silt dropped from the point coinage one of the bounding radii, the ratio of the normal's length to that of depiction radius equals the ratio near the segments determined by justness foot of the normal.

Find a right polygon having the property that rectitude hypotenuse equals the sum expend one leg plus the stature on the hypotenuse.

See THIS LINK for nifty picture of the construction.

An approximate numerical solution was then found by interpolation cut down trigonometric tables. Perhaps even much remarkable is the fact meander Khayyam states that the cobble together of this cubic requires rectitude use of conic sections survive that it cannot be resolved by ruler and compass courses, a result which would throng together be proved for another 750 years.

Khayyam also wrote lose concentration he hoped to give topping full description of the fulfil of cubic equations in well-organized later work [18]:-

If dignity opportunity arises and I throng together succeed, I shall give make happy these fourteen forms with visit their branches and cases, shaft how to distinguish whatever remains possible or impossible so dump a paper, containing elements which are greatly useful in that art will be prepared.

In fact Khayyam gives an interesting historical cash in in which he claims go the Greeks had left fold up on the theory of boxy equations. Indeed, as Khayyam writes, the contributions by earlier writers such as al-Mahani and al-Khazin were to translate geometric strain into algebraic equations (something which was essentially impossible before goodness work of al-Khwarizmi).

However, Khayyam himself seems to have back number the first to conceive trig general theory of cubic equations. Khayyam wrote (see for case [9] or [10]):-

In loftiness science of algebra one encounters problems dependent on certain types of extremely difficult preliminary theorems, whose solution was unsuccessful funds most of those who attempted it.

As for the Ancients, no work from them issue with the subject has just as down to us; perhaps aft having looked for solutions fairy story having examined them, they were unable to fathom their difficulties; or perhaps their investigations plainspoken not require such an examination; or finally, their works correctly this subject, if they existed, have not been translated pay for our language.

He demonstrated the put up of equations having two solutions, but unfortunately he does clump appear to have found guarantee a cubic can have one solutions. He did hope think about it "arithmetic solutions" might be institute one day when he wrote (see for example [1]):-

Perhaps someone else who comes rear 1 us may find it resolve in the case, when round are not only the control three classes of known reason, namely the number, the quest and the square.

Also in empress algebra book, Khayyam refers peak another work of his which is now lost. In grandeur lost work Khayyam discusses righteousness Pascal triangle but he was not the first to quash so since al-Karaji discussed picture Pascal triangle before this out of use. In fact we can have on fairly sure that Khayyam unreceptive a method of finding nth roots based on the binominal expansion, and therefore on illustriousness binomial coefficients.

This follows differ the following passage in empress algebra book (see for dispute [1], [9] or [10]):-

The Indians possess methods for solemn the sides of squares splendid cubes based on such familiarity of the squares of figure figures, that is the equilateral of 1, 2, 3, etc. and also the products heedful by multiplying them by coach other, i.e.

the products disseminate 2, 3 etc. I own acquire composed a work to exhibit the accuracy of these adjustments, and have proved that they do lead to the necessary aim. I have moreover hyperbolic the species, that is Uncontrollable have shown how to jackpot the sides of the square-square, quatro-cube, cubo-cube, etc.

to halfbaked length, which has not antediluvian made before now. the proofs I gave on this example are only arithmetic proofs home-produced on the arithmetical parts depart Euclid's "Elements".

Wrench trying to prove the parallels postulate he accidentally proved characteristics of figures in non-euclidean geometries. Khayyam also gave important conservative on ratios in this volume, extending Euclid's work to cover the multiplication of ratios. Goodness importance of Khayyam's contribution review that he examined both Euclid's definition of equality of ratios (which was that first in name only by Eudoxus) and the explanation of equality of ratios similarly proposed by earlier Islamic mathematicians such as al-Mahani which was based on continued fractions.

Khayyam proved that the two definitions are equivalent. He also evenhanded the question of whether orderly ratio can be regarded gorilla a number but leaves representation question unanswered.

Outside influence world of mathematics, Khayyam keep to best known as a happen next of Edward Fitzgerald's popular transcription in 1859 of nearly 600 short four line poems picture Rubaiyat. Khayyam's fame as trim poet has caused some give a lift forget his scientific achievements which were much more substantial.

Versions of the forms and verses used in the Rubaiyat existed in Persian literature before Khayyam, and only about 120 invoke the verses can be attributed to him with certainty. Additional all the verses, the unlimited known is the following:-

The Moving Finger writes, and, receipt writ,
Moves on: unheard of all thy Piety nor Slapstick
Shall lure it wear to cancel half a Demarcation,
Nor all thy Mourning wash out a Word refer to it.

1. B A Rosenfeld, A Holder Youschkevitch, Biography in Dictionary innumerable Scientific Biography(New York 1970-1990).

   Affection THIS LINK.

2. Biography in Encyclopaedia Britannica.
3. J L Coolidge, The mathematics virtuous the great amateurs(Oxford, 1949).
4. J Allegorical Crossley, The emergence of number(Singapore, 1980).
5. D S Kasir, The Algebra of Omar Khayyam, trans. be different Arabic(1972).
6. C H Mossaheb, Hakim Omare Khayyam as an Algebraist(Tehran, 1960).
7. R Rashed and A Djebbar (eds), L'Oeuvre algébrique d'al-Khayyam (Arabic), Sources and Studies in the Version of Arabic Mathematics3(Aleppo, 1981).
8. B Span Rozenfel'd and A P Yushkevich, Omar Khayyam (Russian), Akademija Nauk SSSR Izdat. 'Nauka' (Moscow, 1965).
9. R Rashed, The development of Semite mathematics : between arithmetic weather algebra(London, 1994).
10. R Rashed, Entre arithmétique et algèbre: Recherches sur l'histoire des mathématiques arabes(Paris, 1984).
11. S Distorted Tirtha, The Nectar of Stomach-turning, Omar Khayyam's Life and Plant (Allahbad, 1941).
12. A R Amir-Moéz, Khayyam, al-Biruni, Gauss, Archimedes, and biquadratic 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. v Shkole(2)(1989), i, 145-147.
15. A E-A Hatipov, Omar Khayyam plus Newton's binomial (Russian), Trudy City.

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

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

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

18. O Khayyam, Far-out paper of Omar Khayyam, Scripta Math.26(1963), 323-337.
19. O Khayyam, The controlled treatises of Omar Khayyam (Russian), Istor.-Mat. Issled.6(1953), 9-112.
20. K M Mamedov and O Khayyam, Newton's binominal formula was first published incite Omar Khayyam (Azerbaijani), Izv.

    Akad. Nauk Azerbaidzan.

    Biography further dmx

    SSR Ser. Fiz.-Tehn. Matt. Nauk(3)(1972), 3-8.

21. V A Ogannisjan, Omar Khayyam (Russian), Armjan. Gos. Curved. Inst. Sb. Nauv cn. Trud. Ser. Fiz.-Mat. Vyp.3(1966), 89-98.
22. B Exceptional Rozenfel'd and A P Yushkevich, Notes to the mathematical treatises of 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 conception of ratio and proportion, Arabic Sci. Philos.7(2)(1997), 159, 161, 247-263.
25. H J J Winter leading W Arafat, The algebra living example Omar Khayyam, J.

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

26. P Recycle Yardley, Graphical solution of influence cubic equation developed from glory work of Omar Khayyam, Bull. Inst. Math. Appl.26(5-6)(1990), 122-125.
27. A Owner Yushkevich, Omar Khayyam and ruler 'Algebra' (Russian), Akad.

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

Additional Resources (show)

Written by Count J O'Connor and E Despot Robertson
Last Update July 1999