소설과 기하학의 역설에 관한 비교연구

초록

This paper studies patterns of geometry in mathematics, paradox by Zeno, abstract notion by Plato, logic by Aristotle and differential and integral calculus by Newton and Leibniz comparing with some novels that contain mathematical stories and events. There are many terms in mathematics we must understand when we explain new ideas for the worldly problems in novels and mathematical and philosophical thoughts. According to the differential and integral systems, for example, we can draw the minimal precisions, we call it infinity, from horizontal events not only in mathematical systems but also in the ways of life. When we demarcate the outline of logics, myth, and even transcendental problems, it is important to know that mathematical idea is to go into the things in itself. That means it is not just categorization, domain and dimension of nature in order to know the ubiquitous patterns. So this paper suggests that we discover the paradox in mathematics with the problems of philosophy and literature. Euclid's Elements has lots of knowledge to count and prove things of the world with axioms. This is the background of this paper where I place axioms in relation to geometry, philosophy, and literature to find out what is the interface. For example, Edwin A. Abbott wrote Flatland: A Romance of Many Dimensions which guides us to the second dimension and third dimension. Flatland was based on the Euclid's axiom. There are many geometric shapes in the novel not only criticizing the culture and people but also thinking mathematical idea of the world. And the shapes of people postulate living things in the second dimension just because of infinity and paradox. The idea of this novel, of course, came from Euclid but it was given to think from the paradox. Therefore, this paper thinks what is the transcendental problems in the world. This is the homologous angle or area where we are living in the different patterns.

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