Ghiyath ad Din Abu AB l Umar Ibn Ibrahim al kayak Nishäpüri 18 May 1048. 4 December 1131 Persian pronounced was a Persian polymath philosopher mathematician astronomer and poet. He also wrote treatises on mechanics geography mineralogy music and Islamic theology. Born in Nishapur at a young age he moved to Samarkand and obtained his education there. Afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times the Treatise on Demonstration of Problems of Algebra which includes a geometric method for solving cubic equations by intersecting hyperbola with a circle. He contributed to a calendar reform. His significance as a philosopher and teacher, and his few remaining philosophical works, has not received the same attention as his scientific and poetic writings. Al Zamakhshari referred to him as the philosopher of the world. Many sources have testified that he taught for decades the philosophy of Avicenna in Nishapur where Khayyam was born and buried and where his mausoleum today remains a masterpiece of Iranian architecture visited by many people every year. Outside Iran and Persian speaking countries, Khayyam has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde 1636.1703 was the first non-Persian to study him. The most influential of all was Edward FitzGerald 1809–83 who made Khayyam the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyam’s rather small number of quatrains Persian in the Rubbia of Omar. Omar Khayyam died in 1131 and is buried in the Khayyam Garden at the mausoleum of Imamzadeh Mahout in Nishapur. In 1963 the mausoleum of Khayyam was constructed on the site by Hooting Siphon. Ghiyath ad Din means the Shoulder of the Faith and implies the knowledge of the Quran Abu’s Fatah Umar Ibn Ibrahim - Abu means father, Fatah means conqueror, 'Umar means life Ibrahim is the name of the father. Khayyam means tent maker it is a byname derived from the father's craft. Nīshāpūrī is the link to his hometown of Nishapur Ghiyāth ad Din Abu’s Fatah Umar ibn Ibrahim al-Khayyam Nīshāpūrī Persian was born in Nishapur, modern-day Iran but then a Seliuqcapital in Khorana which rivaled Cairo or Baghdad in cultural prominence in that era.
Malik Shah
He is thought to have been born into a family of tent-makers which he would make into a play on words later in life 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. He spent part of his childhood in the town of Balkh in present-day northern Afghanistan studying under the well-known scholar Sheikh Muhammad Mansur. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorana region. Throughout his life Omar Khayyam was tireless in his efforts; by day he would teach algebra and geometry, in the evening he would attend the Seljuk court as an adviser of Malik Shah and at night he would study astronomy and complete important aspects of the Jalal calendar. Omar Khayyam’s years in Isfahan were very productive ones, but after the death of the Seljuk Sultan Malik Shah presumably by the Assassins sect the Sultan's widow turned against him as an adviser, and as a result, he soon set out on his Hajj or pilgrimage to Mecca and Medina. He was then allowed to work as a court astrologer, and was permitted to return to Nishapur, where he was renowned for his works, and continued to teach mathematics, astronomy and even medicine. Khayyam Islander was famous during his times as a mathematician. He wrote the influential Treatise on Demonstration of Problems of Algebra 1070 which laid down the principles of algebra part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders. Cubic equation and intersection of conic sections the first page of two-chaptered manuscript kept in Tehran University in the Treatise he wrote on the triangular array of binomial coefficients known as Pascal. In 1077 Khayyam wrote Shah ma acicula min musadarat kitbag Unlades (Explanations of the Difficulties in the Postulates of Euclid) published in English as "On the Difficulties of Euclid's Definitions An important part of the book is concerned with Euclid's famous parallel postulate, which attracted the interest of Thabo ibn Quran Al Chatham had previously attempted a demonstration of the postulate; Khayyam’s attempt was a distinct advance, and his criticisms made their way to Europe, and may have contributed to the eventual development of non-Euclidean geometry. Omar Khayyam created important works on geometry specifically on the theory of proportions. His notable contemporary mathematicians included Al Khaziniand Abu Hakim al Mustafa ibn Ismail al Isfizari Khayyam wrote a book entitled Explanations of the difficulties in the postulates in Euclid's Elements. The book consists of several sections on the parallel postulate Book I on the Euclidean definition of ratios and the Anthyphairtic ratio modern continued fractions Book and on the multiplication of ratios Book III.The first section is a treatise containing some propositions and lemmas concerning the parallel postulate. It has reached the Western world from a reproduction in a manuscript written in 1387 88 AD by the Persian mathematician Tutsi.
Khayyam’s work
Tutsi mentions explicitly that he re-writes the treatise in Khayyam’s own words and quotes Khayyam, saying that "they are worth adding to Euclid's Elements first book after Proposition 28 This proposition states a condition enough for having two lines in plane parallel to one another. After this proposition follows another, numbered 29 which is converse to the previous one the proof of Euclid uses the so called parallel postulate numbered 5 Objection to the use of parallel postulate and alternative view of proposition 29 have been a major problem in foundation of what is now called non-Euclidean geometry.The treatise of Khayyam can be considered as the first treatment of parallels axiom which is not based on petition principia but on a more intuitive postulate. Khayyam refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition. And he, as Aristotle, refuses the use of motion in geometry and therefore dismisses the different by Ibn Hay ham too in a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate. This philosophical view of mathematics see below has had a significant impact on Khayyam’s celebrated approach and method in geometric algebra and in particular in solving cubic equations. In that his solution is not a direct path to a numerical solution and in fact his solutions are not numbers but rather line segmenting this regard Khayyam’s work can be considered the first systematic study and the first exact method of solving cubic equations. In an untitled writing on cubic equations by Khayyam discovered in the 20th century where the above quote appears, Khayyam works on problems of geometric algebra. First is the problem of finding a point on a quadrant of a circle such that when a normal is dropped from the point to one of the bounding radii the ratio of the formal’s length to that of the radius equals the ratio of the segments determined by the foot of the normal. Again in solving this problem, he reduces it to another geometric problem find a right triangle having the property that the hypotenuse equals the sum of one leg i.e. side plus the altitude on the hypotenuse. To solve this geometric problem, he specializes a parameter and reaches the cubic equation . Indeed, he finds a positive root for this equation by intersecting a hyperbola with a circle. This particular geometric solution of cubic equations has been further investigated and extended to degree four equations. Regarding more general equations he states that the solution of cubic equations requires the use of conic sections and that it cannot be solved by ruler and compass methods. A proof of this impossibility was only plausible 750 years after Khayyam died. In this paper Khayyam mentions his will to prepare a paper giving full solution to cubic equations If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared. This refers to the book Treatise on Demonstrations of Problems of Algebra 1070 which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders.
