Omar Khayyam's full name was Ghiyath al-Din Abu'l-Fath Umar ibn Ibrahim Al-Nisaburi al-Khayyami. In Persian langauge, al-Khayyami means 'tent maker'. Khayyam wrote the following lines about his name:
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!
Khayyam's life was driven by the the political incidents of Iran during that time. No scholar or scientist could survive without support from the rulers and politicians.
The Seljuq Turks were tribes that invaded southwestern Asia in the 11th Century and eventually founded an empire that included Mesopotamia, Syria, Palestine, and most of Iran.
In 1070 Khayyam shifted to Samarkand in Uzbekistan.
The Seljuq king made Esfahan the capital of his domains and his grandson Malik-Shah was the ruler of that city from 1073. Khayyam was invited to Esfahan to set up an Observatory there. After this, 18 years of Khayyam's life was devoted to astronomical studies and leading his junior scientists in the observatory.
After Malik-Shah's death in 1092, his second wife took over as ruler and funding to run the Observatory was ceased. Khayyam was under attack from the orthodox Muslims, who believed that Khayyam's questioning mind was against Islamic traditions and faith. But he continued with his scientific work.
One of the most famous of Khayyam's papers incldes this problem:
Find a point on a quadrant of a circle in such manner that when a normal is dropped from the point to one of the bounding radii, the ratio of the normal's length to that of the radius equals the ratio of the segments determined by the foot of the normal.
The same problem can be expressed as : Find a right triangle having the property that the hypotenuse equals the sum of one leg plus the altitude on the hypotenuse.
This problem in turn 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, and using the trigonometric tables. Khayyam stated that the solution of this cubic requires the use of conic sections and that it cannot be solved by ruler and compass methods, a result which would not be proved for another 750 years.
Omar Khayyam's works include Problems of Arithmetic, a book on music and one on algebra.
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