Date: 01/19/97 at 18:03:29 From: Anonymous Subject: Omar Khayyam I need three events about Omar Khayyam, a 1st century mathematican, for a high school report.
Date: 01/20/97 at 14:35:12 From: Doctor Wilkinson Subject: Re: Omar Khayyam Consulting the area on biographies of the MacTutor Math History archive at St. Andrews, we find: http://www-groups.dcs.st-and.ac.uk:80/~history/ Omar Khayyam Born: May 1048 in Nishapur, Persia (now Iran) Died: Dec 1122 in Nishapur, Persia (now Iran) 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 father's trade. Khayyam is best known as a result of Edward Fitzgerald's popular translation in 1859 of nearly 600 short four line poems the Rubaiyat . Khayyam was an outstanding mathematician and astronomer. His work on algebra was known throughout Europe in the Middle Ages, and he also contributed to a calendar reform. He 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 19 century was 365.242196 days, while today it is 365.242190 days. Khayyam refers in his algebra book to another work of his which is now lost. In the lost work Khayyam discusses Pascal's triangle but 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. 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. References: 1. Dictionary of Scientific Biography 2. Biography in Encyclopaedia Britannica 3. D S Kasir, The Algebra of Omar Khayyam, trans. from Arabic (1972). 4. J L Cooidge, The Mathematics of Great Amateurs (New York, 1963), 19-29. 5. C H Mossaheb, Hakim Omare Khayyam as an Algebraist (Tehran, 1960). 6. D Struik, Omar Khayyam, Mathematics Teacher 4 (1958), 280-285. -Doctor Wilkinson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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