Omar Khayyám
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"Khayyam" redirects here. For other uses, see Khayyam (disambiguation).
Omar Khayyam bust in Nishapur, Iran
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| Born | 18 May[1] 1048[2] Nishapur, Khorasan |
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| Died | 4 December[1] 1131 (aged 82/83)[2] Khorasan |
| School | Persian mathematics, Persian poetry, Persian philosophy |
| Main interests | Mathematics, Philosophy, Astronomy, Poetry |
| Sufism and Tariqa |
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Born in Nishapur in North Eastern Iran, at a young age he moved to Samarkand and obtained his education there. Afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle.[4] He contributed to a calendar reform.
His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Al-Zamakhshari referred to him as “the philosopher of the world”. Many sources have testified that he taught for decades the philosophy of Avicenna in Nishapur where Khayyám was born and buried and where his mausoleum today remains a masterpiece of Iranian architecture visited by many people every year.[5]
Outside Iran and Persian speaking countries, Khayyám has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde (1636–1703) was the first non-Persian to study him. The most influential of all was Edward FitzGerald (1809–83),[6] who made Khayyám the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyám's rather small number of quatrains (Persian: رباعیات rubāʿiyāt) in the Rubaiyat of Omar Khayyam.
Omar Khayyám died in 1131 and is buried in the Khayyam Garden at the mausoleum of Imamzadeh Mahruq in Nishapur. In 1963 the mausoleum of Omar Khayyam was constructed on the site by Hooshang Seyhoun.
Contents
Name
غیاث الدین Ghiyāth ad-Din - means "the Shoulder of the Faith" and implies the knowledge of the Quran.ابوالفتح عمر بن ابراهیم Abu'l-Fat'h 'Umar ibn Ibrāhīm - Abu means father, Fat'h means conqueror, 'Umar means life, Ibrahim is the name of the father.
خیام Khayyām - means "tent maker" it is a byname derived from the father's craft.
نیشابورﻯ Nīshāpūrī - is the link to his hometown of Nishapur.
Early life
Ghiyāth ad-Din Abu'l-Fat'h 'Umar ibn Ibrāhīm al-Khayyām Nīshāpūrī (Persian: غیاث الدین ابو الفتح عمر ابراهیم خیام نیشاپوری) was born in Nishapur, in Iran, then a Seljuq capital in Khorasan,[7][8][9] which rivaled Cairo or Baghdad in cultural prominence in that era. He is thought to have been born into a family of tent-makers (khayyāmī "tent-maker"), which he would make into a play on words later in life:Khayyám, who stitched the tents of science,He spent part of his childhood in the town of Balkh (in present-day northern Afghanistan), studying under the well-known scholar Sheikh Muhammad Mansuri. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorasan region. Throughout his life Omar Khayyám was tireless in his efforts; by day he would teach algebra and geometry, in the evening he would attend the Seljuq court as an adviser of Malik-Shah I,[10] and at night he would study astronomy and complete important aspects of the Jalali calendar.
Has fallen in grief's furnace and been suddenly burned,
The shears of Fate have cut the tent ropes of his life,
And the broker of Hope has sold him for nothing!
— Omar Khayyám[4]
Omar Khayyám's years in Isfahan were very productive ones, but after the death of the Seljuq Sultan Malik-Shah I (presumably by the Assassins sect), the Sultan's widow turned against him as an adviser, and as a result, he soon set out on his Hajj or pilgrimage to Mecca and Medina. He was then allowed to work as a court astrologer, and was permitted to return to Nishapur, where he was renowned for his works, and continued to teach mathematics, astronomy and even medicine.[1]
Mathematician
Khayyám Sikander was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders.
Omar Khayyám created important works on geometry, specifically on the theory of proportions. His notable contemporary mathematicians included Al-Khazini and Abu Hatim al-Muzaffar ibn Ismail al-Isfizari[12] 750 years after Khayyám died. In this paper Khayyám mentions his will to prepare a paper giving full solution to cubic equations: "If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared."[18]
Theory of parallels
See also: History of non-Euclidean geometry and Parallel postulate
The first section is a treatise containing some propositions and lemmas concerning the parallel postulate. It has reached the Western world from a reproduction in a manuscript written in 1387-88 AD by the Persian mathematician Tusi. Tusi mentions explicitly that he re-writes the treatise "in Khayyám's own words" and quotes Khayyám, saying that "they are worth adding to Euclid's Elements (first book) after Proposition 28."[13] This proposition[14] states a condition enough for having two lines in plane parallel to one another. After this proposition follows another, numbered 29, which is converse to the previous one.[15] The proof of Euclid uses the so-called parallel postulate (numbered 5). Objection to the use of parallel postulate and alternative view of proposition 29 have been a major problem in foundation of what is now called non-Euclidean geometry.
The treatise of Khayyám can be considered as the first treatment of parallels axiom which is not based on petitio principii but on a more intuitive postulate. Khayyám refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition. And he, as Aristotle, refuses the use of motion in geometry and therefore dismisses the different attempt by Ibn Haytham too.[16] In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate,[17]
Geometric algebra
Omar Khayyam[18]
In an untitled writing on cubic equations by Khayyám discovered in the 20th century,[18] where the above quote appears, Khayyám works on problems of geometric algebra. First is the problem of "finding a point on a quadrant of a circle such that when a normal is dropped from the point to one of the bounding radii, the ratio of the normal's length to that of the radius equals the ratio of the segments determined by the foot of the normal." Again in solving this problem, he reduces it to another geometric problem: "find a right triangle having the property that the hypotenuse equals the sum of one leg (i.e. side) plus the altitude on the hypotenuse.[20] To solve this geometric problem, he specializes a parameter and reaches the cubic equation x3 + 200x = 20x2 + 2000.[18] Indeed, he finds a positive root for this equation by intersecting a hyperbola with a circle.
This particular geometric solution of cubic equations has been further investigated and extended to degree four equations.[21]
Regarding more general equations he states that the solution of cubic equations requires the use of conic sections and that it cannot be solved by ruler and compass methods.[18] A proof of this impossibility was only plausible 750 years after Khayyám died. In this paper Khayyám mentions his will to prepare a paper giving full solution to cubic equations: "If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared."[18]
This refers to the book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe.[19] In particular, he derived general methods for solving cubic equations and even some higher orders.
Binomial theorem and extraction of roots
See also: History of binomial theorem
From the Indians one has methods for obtaining square and cube roots, methods which are based on knowledge of individual cases, namely the knowledge of the squares of the nine digits 12, 22, 32
(etc.) and their respective products, i.e. 2 × 3 etc. We have written a
treatise on the proof of the validity of those methods and that they
satisfy the conditions. In addition we have increased their types,
namely in the form of the determination of the fourth, fifth, sixth
roots up to any desired degree. No one preceded us in this and those
proofs are purely arithmetic, founded on the arithmetic of The Elements.
Omar Khayyam Treatise on Demonstration of Problems of Algebra[22]
Khayyám-Saccheri quadrilateral
Main article: Saccheri quadrilateral
The Saccheri quadrilateral was first considered by Khayyám in the late 11th century in Book I of Explanations of the Difficulties in the Postulates of Euclid.[24] Unlike many commentators on Euclid before and after him (including of course Saccheri), Khayyám was not trying to prove the parallel postulate as such but to derive it from an equivalent postulate he formulated from "the principles of the Philosopher" (Aristotle):- Two convergent straight lines intersect and it is impossible for two convergent straight lines to diverge in the direction in which they converge.[25]
It wasn't until 600 years later that Giordano Vitale made an advance on Khayyám in his book Euclide restituo (1680, 1686), when he used the quadrilateral to prove that if three points are equidistant on the base AB and the summit CD, then AB and CD are everywhere equidistant. Saccheri himself based the whole of his long, heroic, and ultimately flawed proof of the parallel postulate around the quadrilateral and its three cases, proving many theorems about its properties along the way.
Astronomer
Heliocentric Theory
It is sometimes claimed that Khayyam demonstrated that the earth rotates on its axis[32] by presenting a model of the stars to his contemporary al-Ghazali in a planetarium.[33]The other source for the claim that Khayyam believed in heliocentrism are Edward Fitzgerald's popular but anachronistic renderings[34] of Khayyam's poetry, in which the first lines are mistranslated with a heliocentric image of the Sun flinging "the Stone that puts the Stars to Flight".[35]
Calendar reform
Khayyám was a member of a panel that reformed the Iranian calendar. The panel was convened by Seljuk Sultan Malik Shah I, and completed its reforms in 1079, resulting in the Jalali calendar.[36][37]The Jalali calendar remained in force across Greater Iran from the 11th to the 20th centuries. It is the basis of the Iranian calendar which is followed today in Iran and Afghanistan. While the Jalali calendar is more accurate than the Gregorian, it is based on actual solar transit, similar to Hindu calendars, and requires an ephemeris for calculating dates. The lengths of the months can vary between 29 and 31 days depending on the moment when the sun crosses into a new zodiacal area (an attribute common to most Hindu calendars). This meant that seasonal errors were lower than in the Gregorian calendar.
The modern-day Iranian calendar standardizes the month lengths based on a reform from 1925, thus minimizing the effect of solar transits. Seasonal errors are somewhat higher than in the Jalali version, but leap years are calculated as before.
Poetry
Main article: Rubáiyát of Omar Khayyám
Omar Khayyám's poems have been translated to many languages.[39] Many translations were made directly from Persian, more literal than the translation by Edward Fitzgerald.[39] The following samples are from FitzGerald's translation.
The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit,
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
But helpless pieces in the game He plays,
Upon this chequer-board of Nights and Days,
He hither and thither moves, and checks… and slays,
Then one by one, back in the Closet lays.
And, as the Cock crew, those who stood before
The Tavern shouted— “Open then the Door!
You know how little time we have to stay,
And once departed, may return no more.”
A Book of Verses underneath the Bough,
A Jug of Wine, a Loaf of Bread—and Thou,
Beside me singing in the Wilderness,
And oh, Wilderness is Paradise enow.
Myself when young did eagerly frequent
Doctor and Saint, and heard great Argument
About it and about: but evermore
Came out of the same Door as in I went.
With them the Seed of Wisdom did I sow,
And with my own hand labour’d it to grow:
And this was all the Harvest that I reap’d—
“I came like Water, and like Wind I go.”
Into this Universe, and why not knowing,
Nor whence, like Water willy-nilly flowing:
And out of it, as Wind along the Waste,
I know not whither, willy-nilly blowing.
And that inverted Bowl we call The Sky,
Whereunder crawling coop’t we live and die,
Lift not thy hands to It for help—for It
Rolls impotently on as Thou or I.
Views on religion
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The neutrality of this section is disputed. (April 2013) |
"... Fourth, the Sufis, who do not seek knowledge by ratiocination or discursive thinking, but by purgation of their inner being and the purifying of their dispositions. They cleanse the rational soul of the impurities of nature and bodily form, until it becomes pure substance. When it then comes face to face with the spiritual world, the forms of that world become truly reflected in it, without any doubt or ambiguity. This is the best of all ways, because it is known to the servant of God that there is no reflection better than the Divine Presence and in that state there are no obstacles or veils in between. Whatever man lacks is due to the impurity of his nature. If the veil be lifted and the screen and obstacle removed, the truth of things as they are will become manifest and known. And the Master of creatures [the Prophet Muhammad]—upon whom be peace—indicated this when he said: “Truly, during the days of your existence, inspirations come from God. Do you not want to follow them?” Tell unto reasoners that, for the lovers of God, intuition is guide, not discursive thought."The same author goes on by giving other philosophical writings which are totally compatible with the religion of Islam, as the al-Risālah fil-wujūd (الرسالة في الوجود, "Treatise on Being"), written in Arabic, which begin with Quranic verses and asserting that all things come from God, and there is an order in these things. In another work, Risālah jawāban li-thalāth masāʾil (رسالة جوابان لثلاث مسائل, "Treatise of Response to Three Questions"), he gives a response to question on, for instance, the becoming of the soul post-mortem. S.H. Nasr even gives some poetry where he is perfectly in favor of Islamic orthodoxy, but expressing mystical views (God's goodness, the ephemerical state of this life, ...):[5]
—Omar Khayyám[41]
- Thou hast said that Thou wilt torment me,
- But I shall fear not such a warning.
- For where Thou art, there can be no torment,
- And where Thou art not, how can such a place exist?
- The rotating wheel of heaven within which we wonder,
- Is an imaginal lamp of which we have knowledge by similitude.
- The sun is the candle and the world the lamp,
- We are like forms revolving within it.
- A drop of water falls in an ocean wide,
- A grain of dust becomes with earth allied;
- What doth thy coming, going here denote?
- A fly appeared a while, then invisible he became.
"The writings of Omar Khayyam are good specimens of Sufism but are not valued in the West as they ought to be, and the mass of english-speaking people know him only through the poems of Edward Fitzgerald which is unfortunate. It is unfortunate because Fitzgerald is not faithful to his master and model, and at times he lays words upon the tongue of the Sufi which are blasphemous. Such outrageous language is that of the eighty-first quatrain for instance. Fitzgerald is doubly guilty because he was more of a Sufi than he was willing to admit."[42]A French orientalist named Franz Toussaint was so dissatisfied with Fitzgerald's translation (and with some works just translating Fitzgerald from English to French) that he wrote his own directly from the Persian texts, trying to express the spirit of the verses rather than to versify.[43] His translation was published from 1924 to 1979 uninterrupted by Editions d'Art Henri Piazza before that editor disappeared. That translation was itself translated in other languages on Internet sites.
Abdullah Dougan, a modern Naqshbandi Sufi, provides commentary[44] on the role and contribution of Omar Khayyam to Sufi thought. Dougan says that while Omar is a minor Sufi teacher compared to the giants – Rumi, Attar and Sana’i – one aspect that makes Omar’s work so relevant and accessible is its very human scale as we can feel for him and understand his approach. The argument over the quality of Fitzgerald’s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar’s actual material – "Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature".
Philosopher
Khayyám himself rejected any association with the title falsafī "philosopher" in the sense of Aristotelianism and stressed he wishes "to know who I am". In the context of philosophers he was labeled by some of his contemporaries as "detached from divine blessings".[45]
It is now established that Khayyám taught for decades the philosophy of Avicena, especially the Book of Healing, in his home town Nishapur, till his death.[5] In an incident he had been requested to comment on a disagreement between Avicena and a philosopher called Abu'l-Barakāt al-Baghdādī who had criticized Avicena strongly. Khayyám is said to have answered "[he] does not even understand the sense of the words of Avicenna, how can he oppose what he does not know?"[45]
Khayyám the philosopher could be understood from two rather distinct sources. One is through his Rubaiyat and the other through his own works in light of the intellectual and social conditions of his time.[46] The latter could be informed by the evaluations of Khayyám's works by scholars and philosophers such as Abul-Fazl Bayhaqi, Nizami Aruzi, and al-Zamakhshari and Sufi poets and writers Attar of Nishapur and Najm-al-Din Razi.
Mathematical philosophy
As a mathematician, Khayyám has made fundamental contributions to the philosophy of mathematics especially in the context of Persian Mathematics and Persian philosophy with which most of the other Persian scientists and philosophers such as Avicenna, Abū Rayḥān al-Bīrūnī and Tusi are associated. There are at least three basic mathematical ideas of strong philosophical dimensions that can be associated with Khayyám.- Mathematical order: From where does this order issue, and why does it correspond to the world of nature? His answer is in one of his philosophical "treatises on being". Khayyám's answer is that "the Divine Origin of all existence not only emanates wujud "being", by virtue of which all things gain reality, but It is the source of order that is inseparable from the very act of existence."[46]
- The significance of axioms in geometry and the necessity for the mathematician to rely upon philosophy and hence the importance of the relation of any particular science to prime philosophy. This is the philosophical background to Khayyám's total rejection of any attempt to "prove" the parallel postulate, and in turn his refusal to bring motion into the attempt to prove this postulate, as had Ibn al-Haytham, because Khayyám associated motion with the world of matter, and wanted to keep it away from the purely intelligible and immaterial world of geometry.[46]
- Clear distinction made by Khayyám, on the basis of the work of earlier Persian philosophers such as Avicenna, between natural bodies and mathematical bodies. The first is defined as a body that is in the category of substance and that stands by itself, and hence a subject of natural sciences, while the second, called "volume", is of the category of accidents (attributes) that do not subsist by themselves in the external world and hence is the concern of mathematics. Khayyám was very careful to respect the boundaries of each discipline, and criticized ibn al-Haytham in his proof of the parallel postulate precisely because he had broken this rule and had brought a subject belonging to natural philosophy, that is, motion, which belongs to natural bodies, into the domain of geometry, which deals with mathematical bodies.[46]
Gallery
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Persian: "این قافلهٔ عُمر عجب میگذرد" — A line of poetry by the Iranian poet Omar Khayyam in Shikasta Nastaʿlīq.
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A ruba'i of Omar Khayyam in Shikasta Nastaʿlīq.
Legacy
- A lunar crater Omar Khayyam was named after him in 1970.
- A minor planet called 3095 Omarkhayyam, discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980, is named after him.[47]
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