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It’s hard to believe that a civilization consisting of once illiterate nomadic warriors could have a profound impact on the field of mathematics. Yet, many scholars credit the Arabs with preserving much of ancient wisdom. After conquering much of Eastern Europe and Northern Africa the Islamic based Abbasid Empire transitioned away from military conquest into intellectual enlightenment. Florian Cajori speaks of this transition in A History of Mathematics. He states, “Astounding as was the grand march of conquest by the Arabs, still more so was the ease hit which they put aside their former nomadic life adopted a higher civilization, and assumed the sovereignty over cultivated peoples” (Cajori 99). Due to this change in culture,t he Abbasid Empire was able to bridge the gap between two of the most dominant civilizations in mathematic history; the Greeks and the Italians. At the time of Islamic expansion, much of the world had fallen into massive intellectual decline. The quest for knowledge had faltered as civilizations were forced to fight for survival. Islamic scholars played a critical role in retrieving scholarly works from these civilizations and preserving them for future use. According to to Carl Boyer in his book, also titled A History of Mathematics, “Had it not been for the sudden cultural awakening in Islam during the second half of the eighth century, considerably more of ancient science and mathematics would have been lost” (Boyer 227). Islamic scholars did more than just preserve mathematical history. Persian mathematicians, Abu Ja’far Muhammad ibn Musa Al-Khwarizmi, Abu Bakr al-Karaji, and Omar Khayyam, attached rules and provided logical proofs to Grecian geometry thus creating a new field of mathematics called algeb...

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...h is done today. In fact, he is most known as a poet, not a mathematician. Omar Khayyam is most known as the author of some short poems included in Edward Fitzgerald’s Rubaiyat (Texas A&M). The main focus here will be on his geometric proofs regarding the root of third degree polynomials; however, he also pushed for the use of rational numbers and helped to prove the parallel postulate. An article by Texas A&M’s Math Department states, “He discovered exactly what must be showed to prove the parallel postulate, and it was upon these ideas that non-Euclidean geometry was discovered” (Texas A&M). Briefly, the Euclidian parallel postulate is: Given a point and a line, there can only be one line that goes through the point and is parallel to the given line. (See figure below) Khayyam solidified this idea by using a quadrilateral to show the existence of parallel lines.

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