# Omar Khayyam

The Persian astronomer, mathematician, and poet Omar Khayyam (1048-ca. 1132) made important contributions to mathematics, but his chief claim to fame, at least in the last 100 years, has been as the author of a collection of quatrains, the "Rubaiyat."

Omar Khayyam was born in Nishapur in May 1048. His father, Ibrahim, may have been a tentmaker (Khayyam means tentmaker). Omar obtained a thorough education in philosophy and mathematics, and at an early age he attained great fame in the latter field. The Seljuk sultan Jalal-al-Din Malik Shah invited him to collaborate in devising a new calendar, the Jalali or Maliki. Omar spent much of his life teaching philosophy and mathematics, and legends ascribe to him some proficiency in medicine. He died in Nishapur.

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## Astronomical and Mathematical Works

The product of the efforts of Omar and his two collaborators was a set of astronomical tables entitled Al-zij al-Malikshahi after their royal patron. Of this there remains only the table of 100 fixed stars, whose latitude is given for the first year of the Maliki era (1075), and some contradictory descriptions of the Maliki calendar. It is clear that this calendar was intended to retain the basic months of the old Sassanian calendar, in which a year consisted of 12 months of 30 days each plus 5 epagomenal days, with an extra month of 30 days intercalated every 120 years. The intercalation of 30 days in 120 years made the year a Julian year, as in the Julian calendar a day is intercalated every 4 years. The Sassanian and Julian calendars are based on a year of 365.15 days, which is not accurate; Omar and his collaborators devised a modification of the intercalation scheme to overcome this inaccuracy, but the details are obscure.

Omar's work on mathematics is known principally through his commentary on Euclid's Elements and through his treatise On Algebra. In the commentary he is concerned with the foundations of geometry and, in particular, strives to solve the problems of irrational numbers and their relations to rational numbers, in the process very nearly becoming the first to acknowledge irrationals as real numbers; and he examines Euclid's fifth postulate, the "parallel postulate," which distinguishes Euclidean from non-Euclidean geometry. Omar tried to prove the parallel postulate with only the first four postulates by examining a birectangular quadrilateral. The task was an impossible one, but in the course of his attempted proof Omar recognized the logical results of some forms of non-Euclidean geometry. On Algebr a is a classification of equations with proofs of each, some algebraic but most geometric. The most original part is found in his classification of cubic equations, which, following Archimedes, he solved by means of intersecting conic sections.

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## The "Rubaiyat"

Shortly after Omar's death, collections of rubaiyat circulated under his name. These poems consist of 4 lines of 13 syllables each with the rhyme scheme AABA or AAAA; the rhythm within each line is rather free. Rubaiyat had been popular in Persia since the 9th or 10th century as occasional verses extemporaneously recited by all classes of persons; they were used both to express a sort of hedonistic appreciation of life and also Sufi mystical experiences.

Omar's Rubaiyat is known in the West largely through the rather inaccurate paraphrase translation of Edward FitzGerald (1859), which in any case seems to contain a number of non-Khayyamian verses. FitzGerald considerably distorted the original to make it conform to Victorian romanticism; these distortions and the non-Khayyamian verses have led some to believe that Omar was himself a Sufi mystic. Recent discoveries of early-13th-century manuscripts of the Rubaiyat, however, have shown that Omar's poetry follows the other tradition of this form of poetry and celebrates, with humorous skepticism, wit, and poetic skill, the joys of wine and homosexual love.

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## Further Reading on Omar Khayyam

A biography of Omar Khayyam is Harold Lamb, Omar Khayyam: A Life (1934). The most authoritative treatment of his poetry is Arthur John Arberry, ed. and trans., Omar Khayyam (1952). On Omar's contribution to mathematics see Seyyed Hossein Nasr, Science and Civilization in Islam (1968).