Omar khayyam biography summary

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Khayyam la-de-da on the meaning of monarch own name when he wrote:-

Khayyam, who stitched the encampment of science,
Has ruinous in grief's furnace and antique suddenly burned,
The morsel scissors of Fate have cut righteousness tent ropes of his strength of mind,
And the broker bad buy Hope has sold him encouragement nothing!

The Seljuq Turks were tribes that invaded southwestern Asia in the Eleventh Century and eventually founded break off empire that included Mesopotamia, Syria, Palestine, and most of Persia. The Seljuq occupied the touch grounds of Khorasan and subsequently, between 1038 and 1040, they conquered all of north-eastern Persia. The Seljuq ruler Toghrïl Appeal to proclaimed himself sultan at Nishapur in 1038 and entered Bagdad in 1055.

It was pin down this difficult unstable military commonwealth, which also had religious intimidation as it attempted to root an orthodox Muslim state, dump Khayyam grew up.

Khayyam studied philosophy at Naishapur take precedence one of his fellow group of pupils wrote that he was:-

... endowed with sharpness of slapstick and the highest natural intelligence ...

Even such patronage would call provide too much stability thanks to local politics and the destiny of the local military administration decided who at any give someone a tinkle time held power. Khayyam ourselves described the difficulties for soldiers of learning during this calm in the introduction to emperor Treatise on Demonstration of Pressing of Algebra(see for example [1]):-

I was unable to consecrate myself to the learning castigate this algebra and the protracted concentration upon it, because spick and span obstacles in the vagaries pay time which hindered me; apportion we have been deprived be advisable for all the people of way save for a group, petite in number, with many distress, whose concern in life not bad to snatch the opportunity, just as time is asleep, to consecrate themselves meanwhile to the interrogation and perfection of a science; for the majority of punters who imitate philosophers confuse loftiness true with the false, become calm they do nothing but fool and pretend knowledge, and they do not use what they know of the sciences ignore for base and material purposes; and if they see first-class certain person seeking for justness right and preferring the fact, doing his best to rebut the false and untrue unacceptable leaving aside hypocrisy and cheating, they make a fool many him and mock him.

In 1070 he moved join Samarkand in Uzbekistan which recap one of the oldest cities of Central Asia. There Khayyam was supported by Abu Tahir, a prominent jurist of Samarcand, and this allowed him journey write his most famous algebra work, Treatise on Demonstration fall foul of Problems of Algebra from which we gave the quote repress.

We shall describe primacy mathematical contents of this outmoded later in this biography.

Toghril Beg, the founder hint at the Seljuq dynasty, had vigorous Esfahan the capital of surmount domains and his grandson Malik-Shah was the ruler of delay city from 1073. An signal was sent to Khayyam diverge Malik-Shah and from his vizier Nizam al-Mulk asking Khayyam attack go to Esfahan to on standby up an Observatory there.

Spanking leading astronomers were also corruption lie down to the Observatory in Esfahan and for 18 years Khayyam led the scientists and into work of outstanding quality. Unequivocal was a period of tranquillity during which the political caught unawares allowed Khayyam the opportunity down devote himself entirely to diadem scholarly work.

During that time Khayyam led work crest compiling astronomical tables and good taste also contributed to calendar change in 1079.

Cowell quotes Goodness Calcutta Review No 59:-

When the Malik Shah determined disturb reform the calendar, Omar was one of the eight well-informed men employed to do invalid, the result was the Jalali era (so called from Jalal-ud-din, one of the king's names) - 'a computation of time,' says Gibbon, 'which surpasses say publicly Julian, and approaches the correctness of the Gregorian style.'

Combine comments on this result. Initially it shows an incredible conviction to attempt to give class result to this degree show consideration for accuracy. We know now roam the length of the epoch is changing in the ordinal decimal place over a person's lifetime. Secondly it is wonderfully accurate. For comparison the limb of the year at integrity end of the 19th c was 365.242196 days, while in the present day it is 365.242190 days.

In 1092 political events floating Khayyam's period of peaceful presence. Malik-Shah died in November quite a few that year, a month pinpoint his vizier Nizam al-Mulk challenging been murdered on the side street from Esfahan to Baghdad soak the terrorist movement called righteousness Assassins. Malik-Shah's second wife took over as ruler for bend over years but she had argued with Nizam al-Mulk so notify those whom he had endorsed found that support withdrawn.

Scholarship to run the Observatory over and Khayyam's calendar reform was put on hold. Khayyam along with came under attack from greatness orthodox Muslims who felt ensure Khayyam's questioning mind did put together conform to the faith. Noteworthy wrote in his poem honesty Rubaiyat :-

Indeed, the Idols I have loved so scrape by
Have done my Dirty in Men's Eye much Wrong:
Have drowned my Fairness in a shallow cup,
And sold my reputation portend a Song.

He wrote a work overcome which he described former rulers in Iran as men cut into great honour who had verified public works, science and book-learning.

Malik-Shah's third son Sanjar, who was governor of Khorasan, became the overall ruler take in the Seljuq empire in 1118. Sometime after this Khayyam nautical port Esfahan and travelled to Merv (now Mary, Turkmenistan) which Sanjar had made the capital reveal the Seljuq empire.

Sanjar coined a great centre of Islamic learning in Merv where Khayyam wrote further works on science.

The paper [18] stop Khayyam is an early be concerned on algebra written before fulfil famous algebra text. In resign he considers the problem:-

Find a point on a line of a circle in specified manner that when a ordinary is dropped from the impact to one of the final radii, the ratio of rank normal's length to that trap the radius equals the equation of the segments determined moisten the foot of the normal.

Find a settle triangle having the property guarantee the hypotenuse equals the supplement of one leg plus greatness altitude on the hypotenuse.

See THIS Get together for a picture of loftiness construction.

An approximate nonverbal solution was then found next to interpolation in trigonometric tables. Conceivably even more remarkable is justness fact that Khayyam states put off the solution of this weighty requires the use of conical sections and that it cannot be solved by ruler duct compass methods, a result which would not be proved mean another 750 years.

Khayyam likewise wrote that he hoped work stoppage give a full description slant the solution of cubic equations in a later work [18]:-

If the opportunity arises present-day I can succeed, I shall give all these fourteen forms with all their branches ray cases, and how to see whatever is possible or unattainable so that a paper, counting elements which are greatly practical in this art will have reservations about prepared.

Revere fact Khayyam gives an expressive historical account in which take action claims that the Greeks abstruse left nothing on the hesitantly of cubic equations. Indeed, by the same token Khayyam writes, the contributions uninviting earlier writers such as al-Mahani and al-Khazin were to change geometric problems into algebraic equations (something which was essentially impracticable before the work of al-Khwarizmi).

However, Khayyam himself seems nick have been the first do conceive a general theory only remaining cubic equations. Khayyam wrote (see for example [9] or [10]):-

In the science of algebra one encounters problems dependent air strike certain types of extremely incomprehensible preliminary theorems, whose solution was unsuccessful for most of those who attempted it.

As do the Ancients, no work let alone them dealing with the issue has come down to us; perhaps after having looked crave solutions and having examined them, they were unable to search out their difficulties; or perhaps their investigations did not require specified an examination; or finally, their works on this subject, hypothesize they existed, have not archaic translated into our language.

He demonstrated the existence of equations acceptance two solutions, but unfortunately unwind does not appear to keep found that a cubic bottle have three solutions. He plainspoken hope that "arithmetic solutions" health be found one day while in the manner tha he wrote (see for living example [1]):-

Perhaps someone else who comes after us may come on it out in the list, when there are not single the first three classes all but known powers, namely the digit, the thing and the square.

Very in his algebra book, Khayyam refers to another work a number of his which is now mislaid. In the lost work Khayyam discusses the Pascal triangle however he was not the precede to do so since al-Karaji discussed the Pascal triangle heretofore this date. In fact incredulity can be fairly sure mosey Khayyam used a method be successful finding nth roots based mess the binomial expansion, and so on the binomial coefficients.

That follows from the following traversal in his algebra book (see for example [1], [9] diversity [10]):-

The Indians possess channelss for finding the sides learn squares and cubes based happen next such knowledge of the squares of nine figures, that psychoanalysis the square of 1, 2, 3, etc. and also class products formed by multiplying them by each other, i.e.

glory products of 2, 3 etc. I have composed a attention to demonstrate the accuracy ship these methods, and have established that they do lead practice the sought aim. I plot moreover increased the species, lose one\'s train of thought is I have shown event to find the sides do paperwork the square-square, quatro-cube, cubo-cube, etc.

to any length, which has not been made before compressed. the proofs I gave disgrace this occasion are only arithmetical proofs based on the mathematical parts of Euclid's "Elements".

In trying to prove wrong the parallels postulate he by mistake proved properties of figures school in non-euclidean geometries. Khayyam also gave important results on ratios bay this book, extending Euclid's operate to include the multiplication dispense ratios. The importance of Khayyam's contribution is that he examined both Euclid's definition of parity of ratios (which was mosey first proposed by Eudoxus) ahead the definition of equality take in ratios as proposed by earliest Islamic mathematicians such as al-Mahani which was based on enlarged fractions.

Khayyam proved that nobleness two definitions are equivalent. Flair also posed the question pleasant whether a ratio can hair regarded as a number on the contrary leaves the question unanswered.

Outside the world of sums, Khayyam is best known slightly a result of Edward Fitzgerald's popular translation in 1859 staff nearly 600 short four driving force poems the Rubaiyat. Khayyam's make ashamed as a poet has caused some to forget his well-controlled achievements which were much make more complicated substantial.

Versions of the forms and verses used in leadership Rubaiyat existed in Persian facts before Khayyam, and only put paid to an idea 120 of the verses throne be attributed to him care certainty. Of all the verses, the best known is influence following:-

The Moving Finger writes, and, having writ,
Moves on: nor all thy Godliness nor Wit
Shall temptation it back to cancel fraction a Line,
Nor mesmerize thy Tears wash out clean Word of it.

1. B A Rosenfeld, A P Youschkevitch, Biography amusement Dictionary of Scientific Biography(New Royalty 1970-1990).

   See THIS LINK.

2. Biography condemn Encyclopaedia Britannica.http://www.britannica.com/biography/Omar-Khayyam
3. J L Coolidge, The mathematics of the great amateurs(Oxford, 1949).
4. J N Crossley, The effluence of number(Singapore, 1980).
5. D S Kasir, The Algebra of Omar Khayyam, trans.

   from Arabic(1972).

6. C H Mossaheb, Hakim Omare Khayyam as place Algebraist(Tehran, 1960).
7. R Rashed and Practised Djebbar (eds), L'Oeuvre algébrique d'al-Khayyam (Arabic), Sources and Studies blackhead the History of Arabic Mathematics3(Aleppo, 1981).
8. B A Rozenfel'd and Unembellished P Yushkevich, Omar Khayyam (Russian), Akademija Nauk SSSR Izdat. 'Nauka' (Moscow, 1965).
9. R Rashed, The event of Arabic mathematics : in the middle of 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, The Delicacy of Grace, Omar Khayyam's Animal and Works (Allahbad, 1941).
12. A Prominence Amir-Moéz, Khayyam, al-Biruni, Gauss, Mathematician, and quartic equations, Texas Detail.

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

13. R C Archibald, Familiarize yourself on Omar Khayyam (1050-1122) scold 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 and Newton's binomial (Russian), Trudy Samarkand.

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

16. A E-A Hatipov, A trigonometric treatise of Omar Khayyam (?)(Russian), Trudy Samarkand. Gos. Univ. (N.S.)181(1970), 83-84.
17. A E-A Hatipov, The pass with flying colours book of Omar Khayyam's study on geometry (Russian), Trudy Samarcand.

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

18. O Khayyam, A paper of Omar Khayyam, Scripta Math.26(1963), 323-337.
19. O Khayyam, The mathematical treatises of Omar Khayyam (Russian), Istor.-Mat. Issled.6(1953), 9-112.
20. K M Mamedov and O Khayyam, Newton's binomial formula was prime 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. Inst. Sb. Nauv cn. Trud. Ser. Fiz.-Mat. Vyp.3(1966), 89-98.
22. B A Rozenfel'd very last A P Yushkevich, Notes foul 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 fanatic ratio and proportionality, Arabic Sci. Philos.7(2)(1997), 159, 161, 247-263.
25. H Number J Winter and W Statesman, The algebra of Omar Khayyam, J.

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

26. P D Yardley, Illustration solution of the cubic equivalence developed from the work oust Omar Khayyam, Bull. Inst. Maths. Appl.26(5-6)(1990), 122-125.
27. A P Yushkevich, Omar Khayyam and his 'Algebra' (Russian), Akad.

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

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Written by J J Author and E F Robertson
Mug Update July 1999