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Biography: Omar KhayyamOmar Khayyam was born May 1048 in Nishapur, Persia (now Iran), and he died Dec 1122 in Nishapur. Khayyam was a poet as well as a mathematician. He discovered a geometrical method to solve cubic equations by intersecting a parabola with a circle.
Omar Khayyam's full name was Abu al-Fath Omar ben Ibrahim al-Khayyam. A literal translation of his name means 'tent maker' and this may have been his fathers trade. He 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!'
Khayyam studied under the Imam Mowaffak of Naishapur and one of his fellow students, Nizam ul Mulk, wrote that Omar was :-
... endowed with sharpness of wit and the highest natural powers ...
Khayyam is best known as a result of Edward Fitzgerald's popular translation in 1859 of nearly 600 short four line poems the Rubaiyat .
However Khayyam was an outstanding mathematician and astronomer. His work on algebra was known throughout Europe in the Middle Ages, and he also contributed to calendar reform. Cowell quotes The Calcutta Review No 59:-
When the Malik Shah determined to reform the calendar, Omar was one of the eight learned men employed to do it; the result was the Jalali era (so called from Jalal-ud-din, one of the king's names) - 'a computation of time,' says Gibbon, 'which surpasses the Julian, and approaches the accuracy of the Gregorian style.'
Khayyam measured the length of the year as 365.24219858156 days. Two comments on this result. Firstly it shows an incredible confidence to attempt to give the result to this degree of accuracy. We know now that the length of the years is changing in the sixth decimal place over a person's lifetime. Secondly it 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.
In his algebra book, Khayyam refers to another work of his which is now lost. In the lost work Khayyam discusses Pascal's triangle but he was not the first to do so since the Chinese may have discussed Pascal's triangle slightly before this date.
The algebra of Khayyam is geometrical, solving linear and quadratic equations by methods appearing in Euclid's Elements . Khayyam discovered a geometrical method to solve cubic equations. He did this by intersecting a parabola with a circle but, at least in part, these methods had been described by earlier authors such as Abu al-Jud.
Khayyam also gave important results on ratios giving a new definition and extending Euclid's work to include the multiplication of ratios. He poses the question of whether a ratio can be regarded as a number but leaves the question unanswered.
Nizam ul Mulk, a contemporary of Khayyam's, summed up his achievements:-
At Naishapur thus lived and died Omar Khayyam, 'busied,' adds the Vizier, 'in winning knowledge of every kind, and especially in Astronomy, wherein he attained to a very high pre-eminence. Under the Sultanate of Malik Shah, he came to Merv, and obtained great praise for his proficiency in science, and the Sultan showered favors upon him.'
Khayyam's fame as a poet has caused some to forget his scientific achievements which were much more substantial. Versions of the forms and verses used in the Rubaiyat existed in Persian literature before Khayyam, and few of its verses that can be attributed to him with certainty. Of all the verses, the best known is the following:-
The Moving Finger writes; and, having writ,
Moves on : nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
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