Omar Khayyam

OMAR AL-KHAYYAM (1048 – 1131)

A literal translation of the name “al-Khayyam” means “tent maker” and this may have been the trade of Ibrahim his father. Khayyam played on the meaning of his own name when he wrote: 

“Khayyam, who stitched the tents of science,
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 Al-Khayyam was an outstanding mathematician and astronomer. He was also well known as a poet, philosopher, and physician. Khayyam was educated at Nishapur. He traveled to several reputed institutions of learning, including those at Bukhara, Balkh, Samarqand and Isphahan, but he lived in Nishapur and Samarqand for most of his life. 

Khayyam made major contributions in mathematics, particularly in algebra. His work, the Treatise on Demonstration of Problems of Algebra,  contains a complete classification of many algebraic equations based on their complexity and recognizes thirteen different forms of cubic equations. He developed a geometrical approach to solving equations, which involved an ingenious selection of proper conics. He solved cubic equations by intersecting a parabola with a circle. In this work, he expressed that a cubic equation can have more than one solution and also demonstrated the existence of equations having two solutions; but unfortunately he does not appear to have found that a cubic can have three solutions.

In this book, there is also reference to another work by Khayyam on what is now known as Pascal’s triangle, where he used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients.

Khayyam extended Euclid’s work giving a new definition of ratios and included the multiplication of ratios. He also made contributions to the theory of parallel lines. 

Khayyam led work on compiling astronomical tables and he also contributed to calendar reform in 1079. His calendar ‘Al-Tarikh-al-Jalali’ is superior to the Georgian calendar and is accurate to within one day in 3770 years. Specifically, he measured the length of the year as 365.24219858156 days. This result 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.

But now Khayyam is remembered mostly for his poetry, collected in Rubaiyat, even if it is believed that a large part of the 1,000 four-line stanzas can not be attributed to him. His themes involved complex mystical and philosophical thoughts. 

Omar Al-Khayyam’s ten books and thirty monographs have survived. These include four books on mathematics, one on algebra, one on geometry, three on physics, and three books on metaphysics.

Rubaiyat of Omar Khayyam