Khayyam Research Paper

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Omar Khayyam's full name was Ghiyathb al-Din Abu'l-Fath Umar ibn Ibrahim Al-Nisaburi al-Khayyami. Khayyam studied philosophy at Naishapur. He lived in a time that did not make life easy for learned men unless they had the support of a ruler at one of the many courts. However Khayyam was an outstanding mathematician and astronomer and he did write several works including Problems of Arithmetic, a book on music, and one on algebra before he was 25 years old.
In the latter, Khayyam considered the problem of finding a right triangle having the property that the hypotenuse equals the sum of one leg plus the altitude on the hypotenuse. This problem led Khayyam to solve the cubic equation x3 + 200x = 20x2 + 2000 and he found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. Perhaps even more remarkable is the fact that Khayyam states that the solution of this cubic requires the use of conic sections and that it cannot be solved by ruler and compass …show more content…

Other leading astronomers were also brought to the Observatory in Esfahan and for 18 years Khayyam led the scientists and produced work of outstanding quality. It was a period of peace during which the political situation allowed Khayyam the opportunity to devote himself entirely to his scholarly work. During this time, Khayyam led work on compiling astronomical tables and he also contributed to calendar reform in 1079. Khayyam measured the length of the year as 365.24219858156 days. This shows an incredible confidence to attempt to give the result to this degree of accuracy, and it is amazingly accurate. We know now that the length of the year is changing in the sixth decimal place over a person's lifetime. The length of the year in 1900 was 365.242196 days, while in 2000 it was 365.242190

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