Aziz art Augaust 2015.pdf

MathematicianKhayyám was famous during histimes as a mathematician. He wrotethe influential Treatise onDemonstration of Problems ofAlgebra (1070), which laid down theprinciples of algebra, part of thebody of Mathematics that waseventually transmitted to Europe. Inparticular, he derived generalmethods for solving cubic equationsand even some higher orders."Cubic equation and intersection ofconic sections" the first pageof two-chaptered manuscript keptinTehran UniversityIn the Treatise, he wrote on thetriangular array of binomialcoefficients known as Pascal'striangle. In 1077, Khayyám wroteSharh ma ashkala min musadaratkitab Uqlidis (Explanations of theDifficulties in the Postulates ofEuclid) published in English as "Onthe Difficulties of Euclid'sDefinitions". An important part ofthe book is concerned with Euclid'sfamous parallel postulate, whichattracted the interest of Thabit ibnQurra. Al-Haytham had previouslyattempted a demonstration of thepostulate; Khayyám's attempt was adistinct advance, and his criticismsmade their way to Europe, and mayhave contributed to the eventualdevelopment of non-Euclideangeometry.Omar Khayyám created importantworks on geometry, specifically onthe theory of proportions. Hisnotable contemporarymathematicians included Al-Khaziniand Abu Hatim al-Muzaffar ibnIsmail al-IsfizariTheory of parallelsSee also: History of non-Euclideangeometry and Parallel postulateAt the Tomb of Omar Khayyam, byJay HambidgeKhayyám wrote a book entitledExplanations of the difficulties in thepostulates in Euclid's Elements. Thebook consists of several sections onthe parallel postulate , on theEuclidean definition of ratios and theAnthyphairetic ratio (moderncontinued fractions) , and on themultiplication of ratios