Al-Khwarizmi: Algorism, Algorithm and Quadratic Equations - Essay Example

Al-Khwarizmi: Algorism, Algorithm and Quadratic Equations Thesis ment In this reportI want to prove that Abu Ja'far Mohammd ibn Musa Al-Khwarizmi is one of the first and most significant Arabic mathematicians in the ninth century. The scholar's prominent work is considered by many as one of the most important advances in math. His life was not widely written about, in fact, there is very little known about him as a man in contrast to the volumes written about him as a mathematician. In this report I will discuss about his three of many accomplishments namely Algorism, Algorithm and Quadratic Equations. About Al-Khwarizmi The early Arab mathematician and astronomer al-Khwarizmi has been considered by some to be the founder of algebra, a branch of mathematics dealing with equations containing unknown quantities and variables. While this has been disputed, it is certain that his publications on the subject were among the earliest available to the Arab world, and were highly influential among later audiences. (Sen, 2) One of the most well-known early Arab scientists, he wrote his famous treatise, "The Compendious Book on Calculation by Completion and Balancing," by the year 830. Later, this work had a great impact on Western mathematics and science; Latin translations of his work were quite important to scholars and businesspeople during the Middle Ages. Al-Khwarizmi is also known for bringing the Hindu system of fixed numerals to international attention. He wrote an Arab-language text that explained Hindu methods of calculation, which depended upon written numerals rather than the more primitive counting techniques that were widely used at the time. The Beginning Of Algebra: Al-Khwarizmi The 'publication' of the book of al-Khwarizmi at the beginning of the ninth century-between 813 and 833 -is an outstanding event in the history of mathematics. For the first time, one could see the term algebra appearing in a title to designate a distinct mathematical discipline, equipped with a proper technical vocabulary. Muhammad ibn Miss al-Khwarizmi, mathematician, astronomer and distinguished member of the 'House of Wisdom' of Baghdad, had compiled, he wrote, 'a book on algebra and al-muqbala, a concise book recording that which is subtle and important in calculation' (Gandz, 263-277). The event was crucial, and was recognized as such by both ancient and modern historians. Its importance did not escape the mathematical community of the epoch, nor that of the following centuries. This book of al-Khwarizmi did not cease being a source of inspiration and the subject of commentaries by mathematicians, not only in Arabic and Persian, but also in Latin and in the languages of Western Europe until the eighteenth century. But the event appeared paradoxical: to the novelty of the conception, of the vocabulary and of the organization of the book of al-Khwarizmi was contrasted the simplicity of the mathematical techniques described, if one compares them with the techniques in the celebrated mathematical compositions, of Euclid or Diophantus, for example. But this technical simplicity stems precisely from the new mathematical conception of al-Khwarizmi. Whilst one of the elements of his project was found twenty-five centuries before him with the Babylonians, another in the Elements of Euclid, a third in the Arithmetica of Diophantus, no earlier writer had recompiled these elements, and in this manner. But which are these elements, and what is this organization The goal of al-Khwarizmi is clear, never conceived of before: to elaborate a theory of equations solvable through radicals, which can be applied to whatever arithmetical and geometrical problems, and which can help in calculation, commercial transactions, inheritance, the surveying of land etc. Al-Khwarizmi begins by defining the basic terms of this theory which, because of the requirement of resolution by radicals and because of his know-how in this area, was only concerned with equations of the first two degrees. In fact it is about the unknown, casually denoted by root or thing, its square, rational positive numbers, the laws of arithmetic , /, , and equality. The principal concepts introduced next by al-Khwarizmi are the equation of the first degree, the equation of the second degree, the binomials and the associated trinomials, the normal form, algorithmic solutions, and the demonstration of the solution formula. The concept of equation appeared in the book of al-Khwarizmi to designate an infinite class of problems, and not, as with the Babylonians for example, in the course of the solution of one or other problem. Al-Khwarizmi next passed to the determination of algorithmic formulae for the solutions. He made foremost contributions to the fields of algebra, trigonometry, astronomy/astrology, geography and cartography. His methodical and rational approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century. His book On the Calculation with Hindu Numerals written about 825 was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm. Some of his contributions were based on earlier Persian Astronomy Indian numbers and Greek sources. Al-Khwarizmi arranged and corrected Ptolemy's data in geography as regards to Africa and the Middle East. Another major book was his "The Image of the Earth"; translated as Geography, which presented the matches of areas in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa. When his work was copied and moved to Europe through Latin translations, it had a insightful impact on the progression of basic mathematics in Europe. He also wrote on mechanical devices like the clock, astrolabe, and sundial. His other contributions include tables of trigonometric functions, refinements in the geometric representation of conic sections, and aspects of the calculus of two errors. (King) Conclusion Al-Khwarizmi died around the year 850. While his greatest contribution to the sciences may not be as original as that of other important mathematicians, he should be remembered for the influence of his writings across the Arab world, and also in medieval Europe. He is also notable as a foundational scholar for later Arab mathematicians. Works Cited Amartya Sen, How to Judge Globalism: Global Links Have Spread Knowledge and Raised Average Living Standards. but the Present Version of Globalism Needlessly Harms the World's Poorest. The American Prospect. Volume: 13. Issue: 1. 2002. Pg: 2 Gandz, Solomon. "The Sources of al-Khowrizm's Algebra". Osiris 1: 263-277. (1936) King, David A. Al-Khwarizmi and New Trends in Mathematical Astronomy in the Ninth Century. New York University: Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East 2 (1983) Read More