Omar Khayyam

Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshāpūrī was born in Nishapur—a metropolis in Khorasan province of the Seljuk Empire, of Persian stock, in 1048. In medieval Persian texts he is usually simply called Omar Khayyam. The historian Bayhaqi, who was personally acquainted with Khayyam, provides the full details of his horoscope: "he was Gemini, the sun and Mercury being in the ascendant[...]". This was used by modern scholars to establish his date of birth as 18 May 1048. which had earlier been a major center of the Zoroastrian religion. His full name, as it appears in Arabic sources, was Abu’l Fath Omar ibn Ibrahim al-Khayyam. Having memorized much of the Quran at a young age, Khayyam studied religious sciences, Arabic grammar, and literature under Mawlana Qadi Muhammad. He later transferred to the tutelage of Khawjah Abu’l-Hasan al-Anbari to pursue mathematics, astronomy, and cosmological doctrines, including Ptolemy's major work, the Almagest. His gifts were recognized by his early tutors, who sent him to study under Imam Muwaffaq Nishaburi, the greatest teacher of the Khorasan region, who tutored the children of the highest nobility, and Khayyam developed a firm friendship with him through the years. Khayyam was kindly received by the Karakhanid ruler Shams al-Mulk Nasr, who according to Bayhaqi, would "show him the greatest honour, so much so that he would seat [Khayyam] beside him on his throne". He was then invited by the new Sultan Sanjar to Marv, possibly to work as a court astrologer. Omar Khayyam died at the age of 83 in his hometown of Nishapur on 4 December 1131, and he is buried in what is now the Mausoleum of Omar Khayyam. One of his disciples Nizami Aruzi relates the story that sometime during 1112–3 Khayyam was in Balkh in the company of Isfizari (one of the scientists who had collaborated with him on the Jalali calendar) when he made a prophecy that "my tomb shall be in a spot where the north wind may scatter roses over it". Four years after his death, Aruzi located his tomb in a cemetery in a then large and well-known quarter of Nishapur on the road to Marv. As it had been foreseen by Khayyam, Aruzi found the tomb situated at the foot of a garden-wall over which pear trees and apricot trees had thrust their heads and dropped their flowers so that his tombstone was hidden beneath them. ==Mathematics==

Khayyam was famous during his life as a mathematician. His surviving mathematical works include • (i) ''Commentary on the Difficulties Concerning the Postulates of Euclid's Elements'' (), completed in December 1077, • (ii) Treatise On the Division of a Quadrant of a Circle (), undated but completed prior to the Treatise on Algebra, Drawing upon Aristotle's views, he rejects the usage of movement in geometry and therefore dismisses the different attempt by Ibn al-Haytham. Unsatisfied with the failure of mathematicians to prove Euclid's statement from his other postulates, Khayyam tried to connect the axiom with the Fourth Postulate, which states that all right angles are equal to one another. His elaborate attempt to prove the parallel postulate was significant for the further development of geometry, as it clearly shows the possibility of non-Euclidean geometries. The hypotheses of acute, obtuse, and right angles are now known to lead respectively to the non-Euclidean hyperbolic geometry of Gauss-Bolyai-Lobachevsky, to that of elliptic geometry, and to Euclidean geometry. Tusi's commentaries on Khayyam's treatment of parallels made their way to Europe. John Wallis, professor of geometry at Oxford, translated Tusi's commentary into Latin. Jesuit geometer Girolamo Saccheri, whose work (euclides ab omni naevo vindicatus, 1733) is generally considered the first step in the eventual development of non-Euclidean geometry, was familiar with the work of Wallis. The American historian of mathematics David Eugene Smith mentions that Saccheri "used the same lemma as the one of Tusi, even lettering the figure in precisely the same way and using the lemma for the same purpose". He further says that "Tusi distinctly states that it is due to Omar Khayyam, and from the text, it seems clear that the latter was his inspirer." Real number concept This treatise on Euclid contains another contribution dealing with the theory of proportions and with the compounding of ratios. Khayyam discusses the relationship between the concept of ratio and the concept of number and explicitly raises various theoretical difficulties. In particular, he contributes to the theoretical study of the concept of irrational number. Displeased with Euclid's definition of equal ratios, he redefined the concept of a number by the use of a continued fraction as the means of expressing a ratio. Youschkevitch and Rosenfeld argue that "by placing irrational quantities and numbers on the same operational scale, [Khayyam] began a true revolution in the doctrine of number." In the Treatise on the Division of a Quadrant of a Circle Khayyam applied algebra to geometry. In this work, he devoted himself mainly to investigating whether it is possible to divide a circular quadrant into two parts such that the line segments projected from the dividing point to the perpendicular diameters of the circle form a specific ratio. His solution, in turn, employed several curve constructions that led to equations containing cubic and quadratic terms. The Treatise on Algebra contains his work on cubic equations. It is divided into three parts: (i) equations which can be solved with compass and straight edge, (ii) equations which can be solved by means of conic sections, and (iii) equations which involve the inverse of the unknown. He considered three binomial equations, nine trinomial equations, and seven tetranomial equations. For these he could not accomplish the construction of his unknown segment with compass and straight edge. He proceeded to present geometric solutions to all types of cubic equations using the properties of conic sections. The prerequisite lemmas for Khayyam's geometrical proof include Euclid VI, Prop 13, and Apollonius II, Prop 12. However, he acknowledged that the arithmetic problem of these cubics was still unsolved, adding that "possibly someone else will come to know it after us". This particular geometric solution of cubic equations was further investigated by M. Hachtroudi and extended to solving fourth-degree equations. Although similar methods had appeared sporadically since Menaechmus, and further developed by the 10th-century mathematician Abu al-Jud, Khayyam's work can be considered the first systematic study and the first exact method of solving cubic equations. The mathematician Woepcke (1851) who offered translations of Khayyam's algebra into French praised him for his "power of generalization and his rigorously systematic procedure." Binomial theorem and extraction of roots In his algebraic treatise, Khayyam alludes to a book he had written on the extraction of the nth root of natural numbers using a law he had discovered which did not depend on geometric figures. One of Khayyam's predecessors, al-Karaji, had already discovered the triangular arrangement of the coefficients of binomial expansions that Europeans later came to know as Pascal's triangle; Khayyam popularized this triangular array in Iran, so that it is now known as Omar Khayyam's triangle. ==Astronomy==

In 1074–5, Omar Khayyam was commissioned by Sultan Malik-Shah to build an observatory at Isfahan and reform the Persian calendar. There was a panel of eight scholars working under the direction of Khayyam to make large-scale astronomical observations and revise the astronomical tables. The resultant calendar was named in Malik-Shah's honor as the Jalālī calendar, and was inaugurated on 15 March 1079. The observatory itself was disused after the death of Malik-Shah in 1092. The calendar remained in use across Greater Iran from the 11th to the 20th centuries. In 1911, the Jalali calendar became the official national calendar of Qajar Iran. In 1925, this calendar was simplified and the names of the months were modernised, resulting in the modern Iranian calendar. The Jalali calendar is more accurate than the Gregorian calendar of 1582, ==Other works==

Khayyam has a short treatise devoted to Archimedes' principle (in full title, On the Deception of Knowing the Two Quantities of Gold and Silver in a Compound Made of the Two). For a compound of gold adulterated with silver, he describes a method to measure more exactly the weight per capacity of each element. It involves weighing the compound both in air and in water, since weights are easier to measure exactly than volumes. By repeating the same with both gold and silver one finds exactly how much heavier than water gold, silver and the compound were. This treatise was extensively examined by Eilhard Wiedemann who believed that Khayyam's solution was more accurate and sophisticated than that of Khazini and Al-Nayrizi who also dealt with the subject elsewhere. Another short treatise is concerned with music theory in which he discusses the connection between music and arithmetic. Khayyam's contribution was in providing a systematic classification of musical scales, and discussing the mathematical relationship among notes, minor, major and tetrachords. ==Poetry==

calligraphy. The earliest allusion to Omar Khayyam's poetry is from the historian Imad al-Din al-Isfahani, a younger contemporary of Khayyam, who explicitly identifies him as both a poet and a scientist (, 1174). One of the earliest specimens of Omar Khayyam's Rubiyat is from Fakhr al-Din al-Razi. In his work (), he quotes one of his poems (corresponding to quatrain LXII of FitzGerald's first edition). Daya in his writings (, c. 1230) quotes two quatrains, one of which is the same as the one already reported by Razi. An additional quatrain is quoted by the historian Juvayni (, c. 1226–1283). A comparatively late manuscript is the Bodleian MS. Ouseley 140, written in Shiraz in 1460, which contains 158 quatrains on 47 folia. The manuscript belonged to William Ouseley (1767–1842) and was purchased by the Bodleian Library in 1844. in Sarajevo, Bosnia and Herzegovina There are occasional quotes of verses attributed to Khayyam in texts attributed to authors of the 13th and 14th centuries, but these are of doubtful authenticity, so that skeptical scholars point out that the entire tradition may be pseudepigraphic.:307 Five of the quatrains later attributed to Omar Khayyam are found as early as 30 years after his death, quoted in Sindbad-Nameh. While this establishes that these specific verses were in circulation in Omar's time or shortly later, it does not imply that the verses must be his. De Blois concludes that at the least the process of attributing poetry to Omar Khayyam appears to have begun already in the 13th century. and many more have been published since.:312 ==Philosophy==

Khayyam considered himself intellectually to be a student of Avicenna. Religious views A literal reading of Khayyam's quatrains leads to the interpretation of his philosophic attitude toward life as a combination of pessimism, nihilism, Epicureanism, fatalism, and agnosticism. This view is taken by Iranologists such as Arthur Christensen, Hans Heinrich Schaeder, John Andrew Boyle, Edward Denison Ross, Edward Henry Whinfield In addition to his Persian quatrains, J. C. E. Bowen mentions that Khayyam's Arabic poems also "express a pessimistic viewpoint which is entirely consonant with the outlook of the deeply thoughtful rationalist philosopher that Khayyam is known historically to have been." Edward FitzGerald emphasized the religious skepticism he found in Khayyam. In his preface to the Rubáiyát he claimed that he "was hated and dreaded by the Sufis", and denied any pretense at divine allegory: "his Wine is the veritable Juice of the Grape: his Tavern, where it was to be had: his Saki, the Flesh and Blood that poured it out for him." Sadegh Hedayat is one of the most notable proponents of Khayyam's philosophy as agnostic skepticism, and according to Jan Rypka (1934), he even considered Khayyam an atheist. Hedayat (1923) states that "while Khayyam believes in the transmutation and transformation of the human body, he does not believe in a separate soul; if we are lucky, our bodily particles would be used in the making of a jug of wine." Omar Khayyam's poetry has been cited in the context of New Atheism, such as in The Portable Atheist by Christopher Hitchens. Al-Qifti () appears to confirm this view of Khayyam's philosophy. An account of him, written in the thirteenth century, shows him as "versed in all the wisdom of the Greeks," and as wont to insist on the necessity of studying science on Greek lines. Of his prose works, two, which were stand authority, dealt respectively with precious stones and climatology. Beyond question the poet-astronomer was undevout; and his astronomy doubtless helped to make him so. One contemporary writes: "I did not observe that he had any great belief in astrological predictions; nor have I seen or heard of any of the great (scientists) who had such belief. He gave his adherence to no religious sect. Agnosticism, not faith, is the keynote of his works. Among the sects he saw everywhere strife and hatred in which he could have no part...." Persian novelist Sadegh Hedayat says Khayyám from "his youth to his death remained a materialist, pessimist, agnostic. Khayyam looked at all religions questions with a skeptical eye", continues Hedayat, "and hated the fanaticism, narrow-mindedness, and the spirit of vengeance of the mullas, the so-called religious scholars." In the context of a piece entitled On the Knowledge of the Principles of Existence, Khayyam endorses the Sufi path. Other commentators do not accept that Khayyam's poetry has an anti-religious agenda and interpret his references to wine and drunkenness in the conventional metaphorical sense common in Sufism. The French translator J. B. Nicolas held that Khayyam's constant exhortations to drink wine should not be taken literally, but should be regarded rather in the light of Sufi thought where rapturous intoxication by "wine" is to be understood as a metaphor for the enlightened state or divine rapture of baqaa. The view of Omar Khayyam as a Sufi was defended by Bjerregaard, Idries Shah, and Dougan who attributes the reputation of hedonism to the failings of FitzGerald's translation, arguing that Khayyam's poetry is to be understood as "deeply esoteric". On the other hand, Iranian experts such as Mohammad Ali Foroughi and Mojtaba Minovi rejected the hypothesis that Omar Khayyam was a Sufi. The prose works believed to be Khayyam's are written in the Peripatetic style and are explicitly theistic, dealing with subjects such as the existence of God and theodicy. As noted by Bowen these works indicate his involvement in the problems of metaphysics rather than in the subtleties of Sufism. As evidence of Khayyam's faith and/or conformity to Islamic customs, Aminrazavi mentions that in his treatises he offers salutations and prayers, praising God and Muhammad. In most biographical extracts, he is referred to with religious honorifics such as , The Patron of Faith (), and The Evidence of Truth (). He also notes that biographers who praise his religiosity generally avoid making reference to his poetry, while the ones who mention his poetry often do not praise his religious character. For instance, Al-Bayhaqi's account, which antedates by some years other biographical notices, speaks of Omar as a very pious man who professed orthodox views down to his last hour. On the basis of all the existing textual and biographical evidence, the question remains somewhat open, and as a result Khayyam has received sharply conflicting appreciations and criticisms. ==Reception==

in 1997, entitled "850th birth anniversary of Omar Khayyam" The various biographical extracts referring to Omar Khayyam describe him as unequalled in scientific knowledge and achievement during his time. Many called him by the epithet King of the Wise (). Western interest in Persia grew with the Orientalism movement in the 19th century. Joseph von Hammer-Purgstall (1774–1856) translated some of Khayyam's poems into German in 1818, and Gore Ouseley (1770–1844) into English in 1846, but Khayyam remained relatively unknown in the West until after the publication of Edward FitzGerald's Rubaiyat of Omar Khayyam in 1859. FitzGerald's work at first was unsuccessful but was popularised by Whitley Stokes from 1861 onward, and the work came to be greatly admired by the Pre-Raphaelites. In 1872 FitzGerald had a third edition printed which increased interest in the work in America. By the 1880s, the book was extremely well known throughout the English-speaking world, to the extent of the formation of numerous "Omar Khayyam Clubs" and a "fin de siècle cult of the Rubaiyat". Khayyam's poems have been translated into many languages; many of the more recent ones are more literal than that of FitzGerald. FitzGerald's translation was a factor in rekindling interest in Khayyam as a poet even in his native Iran. Sadegh Hedayat in his Songs of Khayyam (Taranehha-ye Khayyam, 1934) reintroduced Khayyam's poetic legacy to modern Iran. Under the Pahlavi dynasty, a new monument of white marble, designed by the architect Houshang Seyhoun, was erected over his tomb. A statue by Abolhassan Sadighi was erected in Laleh Park, Tehran in the 1960s, and a bust by the same sculptor was placed near Khayyam's mausoleum in Nishapur. In 2009, the state of Iran donated a pavilion to the United Nations Office in Vienna, inaugurated at Vienna International Center. In 2016, three statues of Khayyam were unveiled: one at the University of Oklahoma, one in Nishapur and one in Florence, Italy. Over 150 composers have used the Rubaiyat as their source of inspiration. The earliest such composer was Liza Lehmann. FitzGerald rendered Khayyam's name as "Tentmaker", and the anglicized name of "Omar the Tentmaker" resonated in English-speaking popular culture for a while. Thus, Nathan Haskell Dole published a novel called Omar, the Tentmaker: A Romance of Old Persia in 1898. Omar the Tentmaker of Naishapur is a historical novel by John Smith Clarke, published in 1910. "Omar the Tentmaker" is also the title of a 1914 play by Richard Walton Tully in an oriental setting, adapted as a silent film in 1922. US General Omar Bradley was given the nickname "Omar the Tent-Maker" in World War II. The diverse talents and intellectual pursuits of Khayyam captivated many Ottoman and Turkish writers throughout history. Scholars often viewed Khayyam as a means to enhance their own poetic prowess and intellectual depth, drawing inspiration and recognition from his writings. For many Muslim reformers, Khayam's verses provided a counterpoint to the conservative norms prevalent in Islamic societies, allowing room for independent thought and a libertine lifestyle. It reads: The title of the novel The Moving Finger written by Agatha Christie and published in 1942 was inspired by this quatrain of the translation of Rubaiyat of Omar Khayyam by Edward Fitzgerald. In one of his apologetic speeches about the Clinton–Lewinsky scandal, Bill Clinton, the 42nd president of the US, also cites this quatrain. Writer Alan Watts also cites this quatrain in episode 15 of a 1959 television series he hosted called "Eastern Wisdom and Modern Life." Other popular culture references In 1934 Harold Lamb published a historical novel Omar Khayyam. The French-Lebanese writer Amin Maalouf based the first half of his historical fiction novel Samarkand on Khayyam's life and the creation of his Rubaiyat. The sculptor Eduardo Chillida produced four massive iron pieces titled Mesa de Omar Khayyam (Omar Khayyam's Table) in the 1980s. A 1963-1964 serial in The Adventures of Rocky and Bullwinkle and Friends television cartoon has as its macguffin a "Ruby Yacht" (a jewel-encrusted model boat) with Omar Khayyam's name on it. In the South-African born children's novelist Noel Langley's 1937 book The Land of Green Ginger, there is a character called Omar Khayyam, but it is unknown whether this is a reference to the Omar Khayyam The lunar crater Omar Khayyam was named in his honour in 1970, as was the minor planet 3095 Omarkhayyam discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980. Google has released two Google Doodles commemorating him. The first was on his 964th birthday on 18 May 2012. The second was on his 971st birthday on 18 May 2019. == Gallery ==

File:005-a-Ruby-kindles-in-the-vine-810x1146.jpg|"A Ruby kindles in the vine", illustration for FitzGerald's Rubaiyat of Omar Khayyam by Adelaide Hanscom Leeson (c. 1905). File:At the Tomb of Omar Khayyam - by Jay Hambidge.jpg|"At the Tomb of Omar Khayyam" by Jay Hambidge (1911). File:Persian Scholar pavilion in Viena UN (Omar Khayyam).jpg|The statue of Khayyam in United Nations Office in Vienna as a part of Persian Scholars Pavilion donated by Iran. File:Bucureşti - Omar Khayam 3.jpg|Statue of Omar Khayyam in Bucharest File:Madrid - Ciudad Universitaria, Monumento a Omar Jayyam 1.jpg|Monument to Omar Khayyam in Ciudad Universitaria of Madrid ==See also==