Muhammad ben Musa al-Khwarizmi
Muhammad ben Musa al-Khwarizmi was a Persian astrophysicist, geometrician, and geographer. He was born in Persia at around 780 and died around 850. Though his name signifies that his family was originally from the region around Khwarizmi nearby the Aral Sea, historians trust that al-Khwarizmi was congenital in the town of Baghdad, which the current day Iraq. Though diminutive is identified about his cloistered life, al-Khwarizmi’s effort and participation have principally endured the ages discreetly intact. The exclusion is a volume of mathematics in which the novel cannot be established; there is, though, a Latin rendition of his effort as well as additional Arab orientations that quotes the omitted treatise. His algebra was the first book on the systematic solution of linear and quadratic equations. Consequently al-Khwarizmi is to be considered as the discoverer of algebra, a championship he stakes with Diophantus. Latin renditions of his mathematics, on the Indian numerals, introduced the decimal position number system to the western world in the 12th century.
If familiarizing the realm to the Arabic numeral structure is the only achievement that al-Khwarizmi would have fashioned in his life, this would unmoving be satisfactory to grade him as an exceptional of the creation’s great geometricians. Nevertheless, the productive statistician had a correspondingly significant influence that he would put forward. The other scientific task that al-Khwarizmi dispensed with was muqabalah, which decode into the English term balancing or lessening. Conferring to al-Khwarizmi, in his exertion he endeavored to categorize and resolve numerous types of quadratic equivalences as well as provide symmetrical examples for the setups. It is normally supposed that al-Khwarizmi stood predisposed by noe-Babylonian, Greek and Indian foundations with the Indians delivering the arithmetical procedures and the Greeks contributing the custom of demanding proof.
Conferring to al-Khwarizmi, at hand there are three types of numbers; artless numbers, which may be, 4 or 77, the root is the second type, which is the unidentified, x, to be established in a specific arithmetic problem, and the mal, which represent the square of the root in the arithmetic problem. With these descriptions of numbers, al-Khwarizmi categorized problems hooked on six usual forms (non-positive numbers a, b and c);
- Squares equal to roots. Illustration; ax2=bx
- Squares equal to figures. Illustration; ax2=b
- Roots equal to figures. Illustration; ax=b
- Squares and roots equivalents to figures. Illustration; ax2 +bx= c
- Squares and figures equivalent to roots. Illustration; ax2+c=bx
- Roots and figures equivalent to squares. Illustration; ax2=bx+c,
Whereas students of modern mathematics would recognize that all of al-Khwarizmi’s dissimilar arrangements are simply diverse ways of articulating the overall quadratic (ax2+bx+c=0), al-Khwarizmi was incapable of accepting the presence of negative figures. This made it compulsory for al-Khwarizmi to partition what up-to-date arithmeticians consider a subdivision of quadratic equations into numerous smaller subsections that that were mostly consistent with the Arabic assessment of arithmetic. However, even with his limited interpretation of quadratic calculations, al-Khwarizmi was intelligent to make a noteworthy influence regarding the presence of several roots of a quadratic calculation. In particular, al-Khwarizmi arose across this upshot while reviewing his fifth category of the quadratic equation. Using solitary positive figures, the only equation that could perhaps yield two roots is the squares and figures equivalent to roots. Al-Khwarizmi perceived the presence of two roots and exemplified it through the illustrationx2+21=10x. According to the quadratic equation,x is equal to 3 or 7. By investigating with dissimilar values and dissimilar equations of the kind, al-Khwarizmi was intelligent to validate the presence of several roots for quadratic equations. Thus, al-Khwarizmi was intelligent to establish that a quadratic calculation can have additional than one resolution. Plenty of al-Khwarizmi exertion with algebra depicted heavily on the notions of geometry; in many of his evidences and examples, al-Khwarizmi signifies artless figures and roots as length of line parts. The proliferation of roots and numbers characterized by precise rectangles where the roots and figures relate to the lateral lengths of the rectangles and their multiplication embodied the expanse of the rectangle. Acquainted arithmetic terms like completing squares or finding the square off polynomial originates from al-Khwarizmi’s work with geometrically expressing algebraic expressions. For instance, al-Khwarizmi answers x2+10x=39, by the method of completing the square. The following is the geometrics representation of the solution.
In his illustration, he begins by constructing the side lengths x and the area x2. He then creates four rectangles with lateral measurements x and 5/2 and capacity 5x/2. This polygon signifies the x2+10x portion of the calculation. Al-Khwarizmi then finalizes the large square by totaling four minor squares with lateral lengths 5/2 and the capacity 25/4. The entire capacity of the four minor squares is 25. On this equation, he adds 25 to both sides. Therefore, the equation x2+10=39 becomesx2+25=39+25. Simplifying the expression yields (x+5)2=64, which implies that x+5=8 and thereforex=3. This example gives the reason why as he could not calculate for the negatives since it is difficult to create a negative area or length.
Accordingly, it would be appropriate to say that the contemporary mathematics today largely depends on the works of al-Khwarizmi. His invention centered foundation for future Arabs and European Mathematics. The concrete ideas of algebra and his number theory are used all over the world today.
References
Derbyshire, J. ( 2006). Unknown Quantity. Washington D.C.: National Academies Press.
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Calinger, R. (1996). Vita Mahematica. Singapore: Cambridge University Press.
Dixon, M., & Kurdachenko, L. (2011). Algebra and Number Theory. New York: John Wiley & Sons.
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Khuwārizmī, M. M. (1881). The algebra of Mohammed ben Musa. California: Oriental Translation Fund .
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Mohamed, M. (2000). Great Muslim Mathematicians. New Delhi: Penerbit UTM.
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