Omar Khayyam

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/