![\"\"](\"http:\/\/iranthisway.com\/wp-content\/uploads\/2019\/05\/3132222_IMG_0914-1.jpg\")
<\/a><\/figure><\/li><\/a><\/figure><\/li><\/a><\/figure><\/li><\/a><\/figure><\/li><\/a><\/figure><\/li><\/a><\/figure><\/li><\/a><\/figure><\/li><\/ul>\n\n\n\nWho is Omar Khayyam<\/h1>\n\n\n\n
Lived 1048 \u2013 1131.<\/strong><\/p>\n\n\n\n Omar Khayyam’s full name was Ghiyath 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. <\/p>\n\n\n\n In the year 1072 AD, Omar Khayyam documented the most accurate year length ever calculated \u2013 a figure still accurate enough for most purposes in the modern world. Khayyam was an astronomer, astrologer, physician, philosopher, and mathematician: he made outstanding contributions in algebra. His poetry is better known in the West than any other non-Western poet. <\/p>\n\n\n\n The man himself remains something of an enigma. Different biographers\n have documented him as a fun-loving, wine-drinking agnostic; a closet \nZoroastrian; a Sufi Muslim; an orthodox Sunni Moslem; and a follower of \nAncient Greek philosophy. All agree that he was an outstanding \nintellectual.\n\nAdvertisements Omar Khayyam was born on May 18, 1048 in the great trading city of \nNishapur in northern Persia. Today the city is in Iran. Omar\u2019s father \nwas Ebrahim Khayyami, a wealthy physician. Omar\u2019s mother\u2019s name is not \nknown. Some authors have written that Omar\u2019s father earned a living \nmaking tents because Khayyami means tent-maker. However, although many \nEnglish-speakers are named Smith, it does not mean their fathers spent \ntheir days hammering hot metal on an anvil.<\/p>\n\n\n\n Omar\u2019s family were Muslims. His father seems to have been relaxed \nabout religion, employing a mathematician by the name of Bahmanyar bin \nMarzban, a devotee of the ancient Persian religion of Zoroastrianism, to\n tutor Omar. Bahmanyar had been a student of the great physician, \nscientist, and philosopher Avicenna, and he gave Omar a thorough \neducation in science, philosophy, and mathematics. Khawjah al-Anbari \ntaught Omar astronomy, guiding him through Ptolemy\u2019s Almagest<\/a>.<\/p>\n\n\n\n In his early teens Omar worked in his father\u2019s surgery learning about medicine.<\/p>\n\n\n\n Omar Khayyam celebrated his eighteenth birthday in 1066. In the same \nyear, Halley\u2019s comet appeared in the heavens, William the Conqueror\u2019s \nNorman Army invaded England, and Omar\u2019s father Ebrahim died. A few \nmonths after Ebrahim\u2019s death, Omar\u2019s tutor Bahmanyar also died.<\/p>\n\n\n\n It was the end of an era in Omar Khayyam\u2019s life. It was time to put his family\u2019s affairs in order and move on.<\/p>\n\n\n\n Omar Khayyam joined one of the regular caravans making a three month \njourney from Nishapur to the great city of Samarkand, which is now in \nUzbekistan. Samarkand was a center of scholarship, and Khayyam arrived \nthere probably in 1068, aged 20.<\/p>\n\n\n\n In Samarkand he made contact with his father\u2019s old friend Abu Tahir, \nwho was governor and chief judge of the city. Tahir, observing Khayyam\u2019s\n extraordinary talent with numbers, gave him a job in his office. Soon \nKhayyam was given a job in the king\u2019s treasury.<\/p>\n\n\n\n While living in Samarkand, Khayyam made a major advance in algebra. <\/p>\n\n\n\n At high school we learn about equations of the form ax2<\/sup> + bx + c = 0; these are called quadratic equations. Cubic equations are of the form ax3<\/sup> + bx2<\/sup> + cx + d = 0. Naturally, cubic equations are harder to solve than quadratics.<\/p>\n\n\n\n Khayyam conjectured correctly that it is not possible to solve cubic \nequations using the traditional Ancient Greek geometrical tools of \nstraightedge and compass. Other methods are required.<\/p>\n\n\n\n At the age of 22, in 1070, Khayyam published one of his greatest works: Treatise on Demonstration of Problems of Algebra and Balancing<\/em>.\n In it he showed that a cubic equation can have more than one solution. \nHe also showed how the intersections of conic sections such as parabolas\n and circles can be utilized to yield geometric solutions of cubic \nequations. Archimedes<\/a>\n had actually started work in this field over a thousand years earlier, \nwhen he considered the specific problem of finding the ratio of the \nvolume of one part of a sphere to another. Khayyam considered the \nproblem in a more general, methodical way. <\/p>\n\n\n\n In the language of modern mathematics, Khayyam\u2019s solution to the equation x3<\/sup> + a2<\/sup>x = b features a parabola of equation x2<\/sup> = ay, a circle with diameter b\/a2<\/sup>,\n and a vertical line through the intersection point. The solution is \ngiven by the distance on the x-axis between the origin and the (red) \nvertical line. Image by Pieter Kuiper.<\/p>\n\n\n\n Khayyam\u2019s solutions avoided negative coefficients and negative roots \nbecause negative numbers were not acknowledged in Islamic mathematics. \n(Some cultures, however, had incorporated negative numbers into \nmathematics \u2013 for example Brahmagupta<\/a> had introduced negative numbers into Indian mathematics 400 years earlier.)<\/p>\n\n\n\n Although Khayyam\u2019s achievement was magnificent, he was personally \ndisappointed that he needed to utilize geometry to solve cubic equations\n \u2013 he had hoped to discover an algorithm using only algebra. <\/p>\n\n\n\n Treatise on Demonstration of Problems of Algebra and Balancing<\/em> established Khayyam as a mathematician of the first rank, and his reputation spread quickly throughout Persia.<\/p>\n\n\n\n Following Khayyam\u2019s breakthrough there was little significant progress on cubic equations until 1535, when Niccolo Tartaglia<\/a> found general solutions for all cubic equations.<\/p>\n\n\n\n Khayyam\u2019s algebra was not the system of letters and signs we use \ntoday. His algebra was expressed in words. So, where today we write:<\/p>\n\n\n\n Solve for x: <\/p>\n\n\n\n x2<\/sup> + 6 = 5x <\/p>\n\n\n\n Khayyam wrote: What is the amount of a square so that when 6 dirhams \nare added to it, it becomes equal to five roots of that square?<\/p>\n\n\n\n Algebra and Geometry were successfully linked by Pierre de Fermat<\/a> and Ren\u00e9 Descartes<\/a> in the 1600s, resulting in the modern x-y coordinate system. <\/p>\n\n\n\n
<\/p>\n\n\n\nBeginnings<\/h3>\n\n\n\n
Samarkand<\/h3>\n\n\n\n
Omar Khayyam\u2019s Contributions to Science<\/h2>\n\n\n\n
Algebra<\/h3>\n\n\n\n
<\/figure>\n\n\n\nLinking Algebra and Geometry<\/h3>\n\n\n\n