Euclid’s Elements and the Axiomatic Method Essay -- Mathematics Geomet

at that place is no royal road to geometry. Euclid Euclids Elements are predominantly the roughly fundamental concepts of mathematics, but his perspective on geometry was the model for over both millennia. He is believed by many to be the leading mathematics instructor of all time. However, little is known about his life outside of mathematics, or even when he was born or when he died. According to a passage written by Proclus, Euclid probably lived after Ptolemy and the pupils of Plato, but came onwards Archimedes and Eratosthenes. This places his existence sometime around 300 B.C. Euclid is most famous for having denounce the guidelines for geometry and arithmetic written in Euclids Elements, a series of bakers dozen books in which Euclid states definitions, postulates, and theorems for mathematical concepts that are still used today. What is most extraordinary about the Elements is the simple, rational, and very logical structure in which Euclid presents the accumul ated geometrical knowledge from the past several centuries of Greek mathematicians. The manner in which the propositions feature been derived is considered to be the prime model of the axiomatic mode. (Hartshorne 296). Euclids axiomatic method works by starting from a small number of definitions and assumptions at the beginning, so that all the succeeding results are proved by logical conclusion from what has gone before. In essence it is no more than a method of proving that results are correct. Many of Euclids proofs are constructions, all of which can be done using no more than a ruler and a compass and rely only on the theorems and rules of the system. Despite having developed this unyielding system of proofs, Euclid did not actually demonstrate everyt... ... of Nebraska Press, 1991. Blumenthal, Leonard M. A new View of Geometry. San Fransisco W.H. Freeman and Company, 1961. Greenberg, Marvin Jay. Euclidean and Non-Euclidean Geomet ries. New York W.H. Freeman and Company, 1993. Hartshorne, Robin. Geometry, Euclid and Beyond. New York Springer, 2000. Hofstadter, Douglas R.. Gdel, Escher, Bach An Eternal Golden Braid. New York Basic Books, 1975 Narkiewicz, Wladyslaw. The Development of point Number Theory From Euclid to Hardy and Littlewood. Brlin Springer-Verlag, 2000. Singer, David A. Geometry Plane and Fancy. New York Springer, 1998. Internet SourcesJoyce, D. E. Euclids Elements. 1997, online. http//aleph0.clarku.edu/djoyce/java/elements/toc.html (September 18, 2002)