Early Greek Culture & Mathematics
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One of the most well defined and clearest examples of the legacy of the ancient world is that owed to Greek Civilization. Within that legacy, much of the modern world owes a debt in the areas of philosophy, science, education, architecture, social and governmental theory, and the like. An interesting example of a line of thought carried through from the Greek World to the Middle Ages, finally developing at a greater extent in the Renaissance, Reformation, and Age of Discovery, is that of Greek Mathematics. Primarily known for their contributions in the field of geometry, the Greeks nevertheless established the basis for modern mathematical thinking in the fields of logic, real and unreal numbers, and abstract equations. However, since this paper will primarily deal with the cultural aspects of ancient Greece, an emphasis will be placed on the mathematical philosophies rather than the individual contributions by great thinkers and individual personalities.Two questions must be raised, however, within the examination of Greek mathematics. The first must ask about the role that Greek culture as a whole played in the development and evolution of Greek mathematics. Secondly, one should also inquire as to the place of the Greeks within the educational framework itself since it was through that framework that mathematics was transferred within Greek culture and finally down to the contemporary world. Before discussing Greek culture, mathematics, and the resulting influenc
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mination and promulgation of mathematical principles, since only through education were the Greeks able to spread this use of math throughout their own country, as well as to use trade and conquest to spread the principles throughout the ancient world. The Greeks taught that certain intellectual laws were universally valid. In the same vein, the coexistence of mathematical and logical principles were taught almost exclusively within the
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6 Couch, passim.
Greek system. This mathematical and scientific form was directly connected with Greek culture and history.7 Indeed, one might even go so far as to say that it was the very nature of Greek culture that influenced its mathematical thinking. Could an ideology have developed using a pure sense of thinking that required logical principles to exist and applied not just the discovered but the possible discoverable laws of the universe as its basic paradigm?
Thus, the history of Greek mathematics is inexorably tied with cultural and political developments. From the second millennium in the ancient world radical economic and political changes took place. As previously mentioned, the environment on the land now called Greece proved a powerful impetus in the
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