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# Archimedes: The Greatest Mathematician, Essay Example

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Essay

Introduction
Archimedes worn born in Sicily, Italy (277BC-212BC) and was arguably one of the greatest mathematicians that has ever lived. It is considered that during his youth he visited Alexandria in Egypt, a great centre of learning at that time,  here he studied with the successors of Euclid and during this period he invented the Archimedes Screw ( a type of pump); the pump still used in varying parts of the world today.

His main genius and contributions, however, were in the field of Mathematics.  The principal architect of what we know today as Pure Mathematics. His fascination with Geometry and his perfection with methods of integration enabled him to calculate volumes, surface areas and the masses of different bodies. Early works listed by Archimedes illustrated fragments that covered such mathematical areas as: polyhedra, measurements of a circle, plynths and cylinders, surfaces and irregular bodies, mechanics, catoptrics, sphere making and lengths in a year. [1]

The Works of Archimedes

There are a few surviving works (books) of Archimedes, these being: (1)  plane equilibriums (2 books); quadrature of the parabola, the sphere and cylinder (2 books); on spirals; on conoids, on floating bodies and measurements of a circle. A Professor J.L. Heiberg discovered in 1906 a further manuscript of Archimedes called the method.  This offered a valuable perspective on how Archimedes discovered many of his results.  (S. A. Paipetis 2010)[2]

Within the confines of the method it is possible to see the intricate working of how Archimedes developed integral calculus, based upon the theory of proportions by the insertion of polygons into an area that converge to a specific shape.

The Sand reckoner – One of the most remarkable pieces of mathematical genius from Archimedes.  He designed a system that would express numbers  8 X 1063 and claimed that such a number would be large enough to count all the grains of sand that could be placed in the Universe.  A somewhat difficult concept to grasp considering we consider the Universe as infinite. [3]

Spirals –  The concept of a sphere being 4X that of a great circle, he calculates any segments of spheres and further that the surface of a sphere is 2/3rds of a circumscribed cylinder including the base. The work considers the measurement of three dimensional figures.

Floating Bodies – The concept in defining the principles of hydrostatics and the weight of a body immersed in liquid.  He examined the stability of different floating bodies according to different specific gravities. This including the determination of the exact value of ∏.

Conclusion

Oddly enough the real genius of Archimedes work was not fully appreciated until after his death. It was Eutocius that brought many of his works into the light and it was not until the 6th Century AD that full credit was made to the outstanding contribution to mathematics from Archimedes.  Many of his works found their way to the Great Library in Alexandria where they formed the basis of tuition for noted mathematical scholars like Heron, Pappus and Theon.

[1] Netz, Reviel. “The Works of Archimedes: The two books On the sphere and the Cylinder.” In The Works of Archimedes: The two books On the sphere and the Cylinder, by Reviel Netz, Eutocius (of Ascalon.) Archimedes, 12-13. Cambridge: University of Cambridge Press, 2005.

[2] S. A. Paipetis, Marco Ceccarelli. “The Genius of Archimedes – 23 Centuries of Influence on Mathematics .” In The Genius of Archimedes — 23 Centuries of Influence on Mathematics , by Marco Ceccarelli S. A. Paipetis, 380-381. New York: Springer, 2010.

[3] Tubbs, Robert. “What Is a Number?: Mathematical Concepts and Their Origins.” In What Is a Number?: Mathematical Concepts and Their Origins, by Robert Tubbs, 81. Baltimore: John Hopkins University Press, 2010.

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