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Example research essay topic: Twelfth Century Political Turmoil - 2,645 words

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Arabic Mathematics Everybody would agree that mathematics owes a great debt to the Arabs. Just as George Sarton, a famous Harvard professor of history and science wrote in his not less famous Introduction to the History of Science: From the second half of the eighth to the end of the eleventh century, Arabic was the scientific, the progressive language of mankind. When the West was sufficiently mature to feel the need of deeper knowledge, it turned its attention, first of all, not to the Greek sources, but to the Arabic ones. (A al " Daffa p. 65) Before we proceed, it is worth trying to define the period that this essay covers and give an overall description to cover the mathematicians who contributed. The period we cover is easy to describe: it stretches from the end of the eighth century to about the middle of the fifteenth century. Most of the mathematicians we wish to include were Muslims; but some of them were Jews, some Christians, some of other faiths.

Nor were all these mathematicians Arabs, but for convenience we will call our topic "Arab mathematics." Mathematical developments started around 9 th century in Bagdad, but the backgrounds that were underlining the new trend are still not well understood. We are quite sure that Hindu mathematicians have had a significant influence on the process, because of the earlier development of the decimal system and their concept of numerals. Later on, around the twelfth century Europeans have learned about the huge jump forward that Arabs took in mathematics and transformed their achievements in to modern math. Muhammad ibn Musa al-Khawarazmi was the first important Arab mathematician that lived in the ninth century. He gained most of his mathematical knowledge in the East India, where he took the courses of sciences of that time. Muhammad introduced the Hindu numerals; thanks to him we know and understand the concept of Zero.

This number system was later transmitted to the West. Before the Arab numerals that we are all using today, Western civilization had been using Roman numerals, which were enormous in size and very inconvenient in calculations. For example the number 1948 can be written in four figures in the decimal system, but in Roman it would look like MDCCCXLVIII. It is quite clear that even elementary problems would take much time and even more paper using Roman numerals. The Arab numerals have eased the task and therefore were accepted as a standard.

The scientific advances of the West would have been impossible had scientists continued to depend upon the Roman numerals and been deprived of the simplicity and flexibility of the decimal system and its main glory, the zero. Though the Arab numerals were originally a Hindu invention, it was the Arabs who turned them into a workable system; the earliest Arab zero on record dates from the year 873, whereas the earliest Hindu zero is dated 876. For the subsequent four hundred years, Europe laughed at a method that depended upon the use of zero, "a meaningless nothing. " However the decimal was not the only contribution that Arabs made into mathematics, in reality they have given the science much more than that. We never usually think about religion in terms of scientific progress, but in the study of Arab mathematics, we can trace the way religion inspired many of the scientific discoveries. Quran has very specific guidelines about the splitting of the possession among the children of a deceased person. It was a matter of religious beliefs for Arabs to find the way for precise and exact measuring and delineation of lands.

For example, let us say a father left an irregularly shaped piece of land-seventeen acres large-to his six sons, each OAA~ of whom had to receive precisely one-sixth of his legacy. The mathematics that the Arabs had inherited from the Greeks made such a division extremely complicated, if not impossible. It was the search for a more accurate, more comprehensive, and more flexible method that led Khawarazmi to the invention of algebra. According to Professor Sarton, Khawarazmi "influenced mathematical thought to a greater extent than any other medieval writer. , " Both algebra, in the true sense of the term, and the term itself (al-jan) we owe to him. Apart from mathematics, Khawarazmi also did pioneer work in the fields of astronomy, geography and the theory of music. Omar Khayyam who lived in twelfth century was the other man whose achievement helped the Arab civilization and mathematics make a huge leap forward, two centuries after Khawarazmi.

In the West he was famous for its poem Rubayat, but in the East he was primarily known as a mathematician. He has made many discoveries in geometry and further developed the geometry of Descartes. Also the Islamic faith made Arabs to gain more exact knowledge of geography and astronomy. All the Muslims have to perform quite a few religious observances that to involve astronomic geographical implications. For example when a Muslim is praying he has to face Mecca; if he want to perform pilgrimage to Mecca, he has to know where to go.

Among the Arabs who laid the foundations for modern astronomy were Battani (858 - 929) and Biruni (973 - 1048). Battani's astronomical tables were not only adopted enthusiastically by the West, but were in use there until the Renaissance. He was the first to replace the Greek chord by the sine, in trigonometry. His works were translated and published in Europe from the twelfth until the mid-sixteenth century. Professor Sarton considers Biruni "One of the very greatest scientists of all time. " It was he who gave, finally, an accurate determination of latitude and longitude, and who, six hundred years before Galileo, discussed the possibility of the earth's rotation around its own axis. He also investigated the relative speeds of sound and light.

However since much of astronomy is dependent upon mathematics, Arabs have done loads of work in that sphere and truly were the pioneers. In the start of the Middle Ages period, all the instruments were mechanical, like sextant, astrolabe or quadrant. To increase the certainty of results, Arabs had to improve and develop the instruments and therefore came up with remarkable results. The most famous observatory at which these instruments were being used was at Martha, in the thirteenth century, where distinguished astronomers from many countries collaborated-not only Muslim, Christian and Jew, but even Chinese.

It was the latter who were responsible for the otherwise surprising appearance of Arab trigonometry in China. The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medieval. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11 th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and al-Biruni invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Static (1305 - 75), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways. (J L Berggren p. 90) It is obvious that Arabic mathematics had its momentum of glory and then the inevitable crisis came around 13 th and 14 th centuries. The work of the scientist described above are certainly attained the highest point of Arabian mathematics.

After this it was considered the Arabic mathematics ceased. Extreme political turmoil through much of the sub-continent shattered the atmosphere of discovery and learning and led to the stagnation of mathematical developments as scholars contented themselves with duplicating earlier works. Recent discoveries however have found that, despite political turmoil, mathematics continued to a high degree in the Arabian world up to the 16 th century. Arabs avoided the worst of the political upheavals of the subcontinent, and the Kerala School of mathematics flourished for some time, producing some truly remarkable results. These results, the most notable of which are in the field of infinite series expansions of trigonometric functions, are generally inaccurately attributed to great European mathematicians of the 18 th century including Newton, Leibniz and Gregory. However, slowly, this rigid position is shifting somewhat.

There was significant resistance to scientific learning in its totality in Europe until at least the 14 th/ 15 th c and as a result, even though Spain is in Europe, there was little progression of Arabic mathematics throughout the rest of Europe during the Arab period. However, following this period it seems likely Latin translations of Indian and Arabic works will have had an influence. It is possible that the scholars using them did not know the origin of these works. There has also been occasional evidence of European scholars taking results from Indian or Arabic works and presenting them as their own. Actions of this nature highlight the unscrupulous character of some European scholars. It is very sad that a very little recognition have been given to already existent discoveries, even though the Arabic works prevailed in Spain, they did not transmit any further into Europe, which was still to fully awaken and probably resisted the works, and many were subsequently lost.

However ultimately a few Latin translations of Arabic works did flow into wider Europe, causing a step towards the renaissance. To summarize, the main reasons for the neglect of Arabic mathematics seem to be religious, cultural and psychological. Primarily it is because of an ideological choice. R Rashed mentions a concept of modernism vs. tradition.

Furthermore Arabic mathematics is criticized because it lacks rigor and is only interested in practical aims (which we know to be incorrect). Ultimately it is fundamentally important for historians to be neutral, (that includes Indian historians who may go too far the 'other way') and this has not always been the case, and indeed seems to still persist in some quarters. In terms of consequences of the Euro centric stance, it has undoubtedly resulted in a cultural divide and 'angered' non-Europeans scholars. There is an unhealthy air of European superiority, which is potentially quite politically dangerous, and scientifically unproductive. In order to maximise our knowledge of mathematics we must recognise many more nations as being able to provide valuable input, this statement is also relevant to past works.

Eurocentrism has led to an historical 'imbalance', which basically means scholars are not presenting an accurate version of the history of the subject, which I view as unacceptable. Furthermore, it is vital to point out that European colonisation of Arabian territories most certainly had an extremely negative effect on the progress of indigenous Arabic science. But Arabic mathematics was slowly regaining its strength; there is no doubt that Arabs have made mathematics to gain a new dynamic quality. We find this in Biruni's trigonometry, where numbers became elements of function, and in Khawarazmi's algebra, where the algebraic symbols contain within themselves potentialities for the infinite. What is significant about this development is that it reveals an intuitive correspondence between mathematics and religion. The Quran does not present the universe as finally created or as a finished "article. " Rather, God keeps re-creating it at every moment of existence.

In other words, creation is an ever-living process, and the world is not static but dynamic. This dynamic character, inherent in Islam, is amply manifested in Arab mathematics. Most of the translations into Arabic at this time have been made by mathematicians such as named above, not by the language experts that know nothing about mathematics, and the need of translations was motivated by the extensive research that was taking place at that time. We have to realized that translation was not done just to be done, but were the part of the Arabic research. The most important Greek and Arabic mathematical texts, which were translated, are listed below: Of Euclid's works, the Elements, the Data, the Optics, the Phenomena, and On Divisions were translated. Of Archimedes' works only two - Sphere and Cylinder and Measurement of the Circle - are known to have been translated, but these were sufficient to stimulate independent researches from the 9 th to the 15 th century.

On the other hand, virtually all of Apollonius's works were translated, and of Diophantus and Menelaus one book each, the Arithmetic and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of Ptolemy's Almagest furnished important astronomical material. (R Rashed p. 115) Despite the fact that Arabic scientists are mostly famous for their contribution in algebra and number systems, they have made a lot work in geometry, trigonometry and mathematical astronomy. Ibrahim ibn Sinan who was born in 908, introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Arabic higher geometry in the Islamic world. These mathematicians, and in particular al-Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. Omar Khayyam combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. That ibn Quran undertook both theoretical and observational work in astronomy.

Al-Battani (born 850) made accurate observations, which allowed him to improve on Ptolemy's data for the sun and the moon. Nasir al-Din al-Tusi (born 1201), like many other Arabic mathematicians, based his theoretical astronomy on Ptolemy's work but al-Tusi made the most significant development of Ptolemy's model of the planetary system up to the development of the heliocentric model in the time of Copernicus. Many of the Arabic mathematicians produced tables of trigonometric functions as part of their studies of astronomy. These include Ulugh Beg (born 1393) and al-Kashi. The construction of astronomical instruments such as the astrolabe was also a speciality of the Arabs. Al-Mahani used an astrolabe while Ahmed (born 835), al-Khan (born 900), Ibrahim ibn Sinan, al-Quhi, Abu Nasr Mansur (born 965), al-Biruni, and others, all wrote important treatises on the astrolabe.

Share al-Din al-Tusi (born 1201) invented the linear astrolabe. Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas, which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth, and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks In conclusion, it is clear that Arab mathematicians, besides passing on to the West the Hindu and Greek legacies, have developed most branches of trigonometry and astronomy, have given us algebra, have invented many astronomical instruments, and have shown that science, instead of being a denial of faith, can be its instrument if not its affirmation. Words 2665 Bibliography: A al " Daffa, The Muslim contribution to mathematics (London, 1978). J L Berggren, Episodes in the Mathematics of Medieval Islam (1986).

D S Kabir (ed. and trans. ), The Algebra of Omar Khayyam (1931, reprinted 1972). E S Kennedy et al. , Studies in the Islamic Exact Sciences (1983). R Rashed, The development of Arabic mathematics: between arithmetic and algebra (London, 1994). F Rosen (ed.

and trans. ), The Algebra of Mohammed ben Musa (1831, reprinted 1986). M Zarruqi, Fractions in the Moroccan mathematical tradition between the 12 th and 15 th centuries A. D. as found in anonymous manuscripts. (Arabic), in Deuxieme Colloque Maghreb in sur l'Histoire des Mathematiques Arabes, Tunis 1988 (Tunis, 1990), A 97 -A 109.

R Rashed, The development of Arabic mathematics: between arithmetic and algebra (London, 1994). J L Berggren, Episodes in the Mathematics of Medieval Islam (1986).


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Research essay sample on Twelfth Century Political Turmoil

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