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Omar Khayyam
Ghiyath al-Din Abu al-Fatḥ ʿUmar ibn Ibrahim Nisaburi (b. May 18, 1048, Nishapur, Khorasan, Seljuk Empire [today in Iran] – d. December 4, 1131, Nishapur, Khorasan, Seljuk Empire [today in Iran]), commonly known as Omar Khayyam was a Persian polymath, known for his contributions to mathematics, astronomy, philosophy, and poetry. He was born in Nishapur, the initial capital of the Seljuk Empire. As a scholar, he was contemporary with the rule of the Seljuk dynasty around the time of the First Crusade.
As a mathematician, Omar Khayyam is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics. Khayyam also contributed to the understanding of the parallel axiom. As an astronomer, he calculated the duration of the solar year with remarkable precision and accuracy, and designed the Jalali calendar, a solar calendar with a very precise 33-year intercalation cycle that provided the basis for the Persian calendar that is still in use after nearly a millennium.
There is a tradition of attributing poetry to Omar Khayyam, written in the form of quatrains (ruba'iyat). This poetry became widely known to the English-reading world in a translation by Edward FitzGerald (Rubaiyat of Omar Khayyam, 1859), which enjoyed great success in the Orientalism of the fin de siecle -- the end of the century.
Omar Khayyam was born, of Khorasani Persian ancestry, in Nishapur in 1048. In medieval Persian texts he is usually simply called Omar Khayyam. Although open to doubt, it has often been assumed that his forebears followed the trade of tent-making, since Khayyam means tent-maker in Arabic.
Khayyam's boyhood was spent in Nishapur, a leading metropolis under the Great Seljuq Empire, and it had been a major center of the Zoroastrian religion. His full name, as it appears in the Arabic sources, was Abu’l Fath Omar ibn Ibrahim al-Khayyam. 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. Omar made a great friendship with him through the years. Khayyam was also taught by the Zoroastrian mathematician, Abu Hassan Bahmanyar bin Marzban. After studying science, philosophy, mathematics and astronomy at Nishapur, about the year 1068 he traveled to the province of Bukhara, where he frequented the renowned library of the Ark.
In about 1070, Khayyam moved to Samarkand, where he started to compose his famous treatise on algebra under the patronage of Abu Tahir Abd al-Rahman ibn ʿAlaq, the governor and chief judge of the city. Omar Khayyam was kindly received by the Karakhanid ruler Shams al-Mulk Nasr.
In 1073–4, peace was concluded with Sultan Malik Shah I who had made incursions into Karakhanid dominions. Khayyam entered the service of Malik-Shah in 1074–5 when he was invited by the Grand Vizier Nizam al-Mulk to meet Malik Shah in the city of Marv. Khayyam was subsequently commissioned to set up an observatory in Isfahan and lead a group of scientists in carrying out precise astronomical observations aimed at the revision of the Persian calendar. The undertaking began probably in 1076 and ended in 1079 when Omar Khayyam and his colleagues concluded their measurements of the length of the year, reporting it as 365.24219858156 days. Given that the length of the year is changing in the sixth decimal place over a person's lifetime, this is outstandingly accurate. For comparison the length of the year at the end of the 19th century was 365.242196 days, while today it is 365.242190 days.
After the death of Malik-Shah and his vizier (murdered, it is thought, by the Ismaili order of Assassins), Omar fell from favor at court, and as a result, he soon set out on his pilgrimage to Mecca. A possible ulterior motive for his pilgrimage was a public demonstration of his faith with a view to allaying suspicions of skepticism and confuting the allegations of unorthodoxy (including possible sympathy or adherence to Zoroastrianism) levelled at him by a hostile clergy. He was then invited by the new Sultan Sanjar to Marv, possibly to work as a court astrologer. He was later allowed to return to Nishapur owing to his declining health. Upon his return, he seems to have lived the life of a recluse.
Omar Khayyam died at the age of 83 in his hometown of Nishapur on December 4, 1131. 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 Al-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 peach trees had thrust their heads and dropped their flowers so that his tombstone was hidden beneath them.
Khayyam was famous during his life as a mathematician. His surviving mathematical works include: A commentary on the difficulties concerning the postulates of Euclid's Elements (Risāla fī šarḥ mā aškala min muṣādarāt kitāb Uqlīdis, completed in December 1077); On the division of a quadrant of a circle (Risālah fī qismah rub‘ al-dā’irah); and On proofs for problems concerning Algebra (Maqāla fi l-jabr wa l-muqābala, most likely completed in 1079). He furthermore wrote a treatise on the binomial theorem, which has been lost.
A part of Khayyam's commentary on Euclid's Elements deals with the parallel axiom. The treatise of Khayyam can be considered the first treatment of the axiom not based on petitio principii, but on a more intuitive postulate. Khayyam refutes the previous attempts by other mathematicians to prove the proposition, mainly on grounds that each of them had postulated something that was by no means easier to admit than the Fifth Postulate itself. Drawing upon Aristotle's views, he rejects the usage of movement in geometry and therefore dismisses the different attempt by Al-Haytham. Unsatisfied with the failure of mathematicians to prove Euclid's statement from his other postulates, Omar tried to connect the axiom with the Fourth Postulate, which states that all right angles are equal to one another.
Khayyam was the first to consider the three distinct cases of acute, obtuse, and right angle for the summit angles of a Khayyam-Saccheri quadrilateral. After proving a number of theorems about them, he showed that Postulate V follows from the right angle hypothesis, and refuted the obtuse and acute cases as self-contradictory. 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 Riemannian geometry, and to Euclidean geometry.
Tusi's commentaries on Khayyam's treatment of parallels made its way to Europe. John Wallis, a professor of geometry at Oxford University, 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.
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 contributed to the theoretical study of the concept of irrational numbers. Displeased with Euclid's definition of equal ratios, he redefined the concept of a number by the use of a continuous fraction as the means of expressing a ratio. by placing irrational quantities and numbers on the same operational scale, Khayyam began a revolution in the doctrine of number.
Because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered the precursor of Descartes in the invention of analytic geometry. 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.
Khayyam seems to have been the first to conceive a general theory of cubic equations and the first to geometrically solve every type of cubic equation, so far as positive roots are concerned. 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.
Khayyam produced an exhaustive list of all possible equations involving lines, squares, and cubes. He considered three binomial equations, nine trinomial equations, and seven tetranomial equations. For the first and second degree polynomials, he provided numerical solutions by geometric construction. He concluded that there are fourteen different types of cubics that cannot be reduced to an equation of a lesser degree. 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.
In effect, Khayyam's work is an effort to unify algebra and geometry. Khayyam's work can be considered the first systematic study and the first exact method of solving cubic equations.
In 1074–5, Omar Khayyam was commissioned by Sultan Malik-Shah to build an observatory of 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. Recalibrating the calendar fixed the first day of the year at the exact moment of the passing of the Sun's center across vernal equinox. This marks the beginning of spring or Nowruz, a day in which the Sun enters the first degree of Aries before noon. The resultant calendar was named in Malik-Shah's honor as the Jalali calendar and was inaugurated on March 15, 1079. The observatory itself was disused after the death of Malik-Shah in 1092.
The Jalali calendar was a true solar calendar where the duration of each month is equal to the time of the passage of the Sun across the corresponding sign of the Zodiac. The calendar reform introduced a unique 33-year intercalation cycle. As indicated by the works of Khazini, Khayyam's group implemented an intercalation system based on quadrennial and quinquennial leap years. Therefore, the calendar consisted of 25 ordinary years that included 365 days, and 8 leap years that included 366 days. 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 modernized, resulting in the modern Iranian calendar. The Jalali calendar is more accurate than the Gregorian calendar of 1582 with an error of one day accumulating over 5,000 years, compared to one day every 3,330 years in the Gregorian calendar.
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, Khayyam 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.
Another short treatise is concerned with music theory in which Khayyam 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.
The poetry attributed to Omar Khayyam has contributed greatly to his popular fame in the modern period as a direct result of the extreme popularity of the translation of such verses into English by Edward FitzGerald (1859). FitzGerald's Rubaiyat of Omar Khayyam contains loose translations of quatrains from the Bodleian manuscript. It enjoyed such success in the fin de siecle period that a bibliography compiled in 1929 listed more than 300 separate editions, and many more have been published since.
The earliest allusion to Omar Khayyam's poetry is from the historian Imad ad-Din al-Isfahani, a younger contemporary of Khayyam, who explicitly identifies him as both a poet and a scientist (Kharidat al-qasr, 1174). One of the earliest specimens of Omar Khayyam's Rubaiyat is from Fakhr al-Din Razi. In his work Al-tanbih ‘ala ba‘d asrar al-maw‘dat fi’l-Qur’an (ca. 1160), Fakhr al-Din Razi quotes one of Khayyam's poems (corresponding to quatrain LXII of FitzGerald's first edition). Daya in his writings (Mirsad al-‘Ibad, ca. 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 (Tarikh-i Jahangushay ca. 1226–1283). In 1340, Jajarmi includes thirteen quatrains of Khayyam in his work containing an anthology of the works of famous Persian poets (Munis al-ahrār).
Five of the quatrains later attributed to Omar 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 doesn't 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.
In addition to the Persian quatrains, there are twenty-five Arabic poems attributed to Khayyam which are attested to by historians such as al-Isfahani, Shahrazuri (Nuzhat al-Arwah, ca. 1201–1211), Qifti (Tārikh al-hukamā, 1255), and Hamdallah Mustawfi (Tarikh-i guzida, 1339).
There are a number of other Persian scholars who occasionally wrote quatrains, including Avicenna (Ibn Sina), Ghazzali, and Tusi. They conclude that it is possible that, for Khayyam, poetry was an amusement of his leisure hours. The poetry of the Persian scholars seems often to have been the work of scholars and scientists who composed them, perhaps, in moments of relaxation to edify or amuse the inner circle of their disciples.
Five of the quatrains attributed to Omar 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.
In addition to the Persian quatrains, there are twenty-five Arabic poems attributed to Khayyam which are attested by historians such as al-Isfahani, Shahrazuri (Nuzhat al-Arwah, ca. 1201–1211), Qifti (Tārikh al-hukamā, 1255), and Hamdallah Mustawfi (Tarikh-i guzida, 1339).
Khayyam from his youth to his death remained a materialist, pessimist, agnostic. Khayyam looked at all religions questions with a skeptical eye 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. Omar Khayyam could see in Sufism an ally against orthodox religiosity. 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. 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.
Thomas Hyde was the first European to call attention to Khayyam and to translate one of his quatrains into Latin (Historia religionis veterum Persarum eorumque magorum, 1700). 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 of in 1859. FitzGerald's work at first was unsuccessful but was popularized 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 that it led to the formation of numerous "Omar Khayyam Clubs" and a fin de siècle (end of the century) 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 Omar'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 Omar Khayyam's 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 the 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 Omar'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. United States General Omar Bradley was given the nickname "Omar the Tent-Maker" in World War II.
The quatrain by Omar Khayyam known as "The Moving Finger", in the form of its translation by the English poet Edward Fitzgerald is one of the most popular quatrains in the Anglosphere. 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. Martin Luther King also cites this quatrain of Omar Khayyam in one of his speeches "Beyond Vietnam: A Time to Break Silence":
In one of his apologetic speeches about the Clinton-Lewinsky scandal, Bill Clinton, the 42nd president of the US, also cites this quatrain.
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.
The lunar crater Omar Khayyam was named in honor Omar Khayyam in 1970, as was the minor planet 3095 Omarkhayyyam discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980.
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Omar Khayyam, Arabic in full Ghiyath al-Din Abu al-Fatḥ ʿUmar ibn Ibrahim al-Nisaburi al-Khayyami, (b. May 18, 1048, Neyshabur [also spelled Nishapur], Khorasan [now Iran] — d. December 4, 1131, Neyshabur, Khorasan [now Iran]), Persian mathematician, astronomer, and poet, renowned in his own country and time for his scientific achievements but chiefly known to English-speaking readers through the translation of a collection of his robaʿiyat (“quatrains”) in The Rubaiyat of Omar Khayyam (1859), by the English writer Edward FitzGerald.
His name Khayyam (“Tentmaker”) may have been derived from his father’s trade. He received a good education in the sciences and philosophy in his native Neyshabur before traveling to Samarkand (now in Uzbekistan), where he completed the algebra treatise, Risalah fiʾl-barahin ʿala masaʾil al-jabr waʾl-muqabalah (“Treatise on Demonstration of Problems of Algebra”), on which his mathematical reputation principally rests. In this treatise he gave a systematic discussion of the solution of cubic equations by means of intersecting conic sections. Perhaps it was in the context of this work that he discovered how to extend Abu al-Wafa's results on the extraction of cube and fourth roots to the extraction of nth roots of numbers for arbitrary whole numbers n.
Khayyam made such a name for himself that the Seljuq Sultan Malik-Shah invited him to Esfahan to undertake the astronomical observations necessary for the reform of the calendar. To accomplish this an observatory was built there, and a new calendar was produced, known as the Jalali calendar. Based on making 8 of every 33 years leap years, it was more accurate than the present Gregorian calendar, and it was adopted in 1075 by Malik-Shah.
In Eṣfahan, Khayyam also produced fundamental critiques of Euclid's theory of parallels as well as his theory of proportion. In connection with the former his ideas eventually made their way to Europe, where they influenced the English mathematician John Wallis (1616–1703); in connection with the latter he argued for the important idea of enlarging the notion of number to include ratios of magnitudes (and hence such irrational numbers as the square root of 2 Square root ofand π).
Khayyam's years in Esfahan were very productive ones, but after the death of his patron in 1092 the sultan’s widow turned against him, and soon thereafter Omar went on a pilgrimage (a hajj) to Mecca. He then returned to Neyshabur where he taught and served the court as an astrologer. Philosophy, jurisprudence, history, mathematics, medicine, and astronomy are among the subjects mastered by this brilliant man.
Omar’s fame in the West rests upon the collection of robaʿiyat, or “quatrains,” attributed to him. (A quatrain is a piece of verse complete in four lines, usually rhyming aaaa or aaba; it is close in style and spirit to the epigram.) Omar’s poems had attracted comparatively little attention until they inspired FitzGerald to write his celebrated The Rubáiyát of Omar Khayyám, containing such now-famous phrases as “A Jug of Wine, a Loaf of Bread—and Thou,” “Take the Cash, and let the Credit go,” and “The Flower that once has blown forever dies.” These quatrains have been translated into almost every major language and are largely responsible for coloring European ideas about Persian poetry. Some scholars have doubted that Omar wrote poetry. His contemporaries took no notice of his verse, and not until two centuries after his death did a few quatrains appear under his name. Even then, the verses were mostly used as quotations against particular views ostensibly held by Omar, leading some scholars to suspect that they may have been invented and attributed to Omar because of his scholarly reputation.
Each of Omar’s quatrains forms a complete poem in itself. It was FitzGerald who conceived the idea of combining a series of these robaʿiyat into a continuous elegy that had an intellectual unity and consistency. FitzGerald’s ingenious and felicitous paraphrasing gave his translations a memorable verve and succinctness. They are, however, extremely free translations, and more recently several more faithful renderings of the quatrains have been published.
The verses translated by FitzGerald and others reveal a man of deep thought, troubled by the questions of the nature of reality and the eternal, the impermanence and uncertainty of life, and man’s relationship to God. The writer doubts the existence of divine providence and the afterlife, derides religious certainty, and feels keenly man’s frailty and ignorance. Finding no acceptable answers to his perplexities, he chooses to put his faith instead in a joyful appreciation of the fleeting and sensuous beauties of the material world. The idyllic nature of the modest pleasures he celebrates, however, cannot dispel his honest and straightforward brooding over fundamental metaphysical questions.
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https://www.britannica.com/biography/Omar-Khayyam-Persian-poet-and-astronomer
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