금속비의 확장 가능성에 관한 연구 = A Study on the Possibility of Expanding the Metallic Mean

다국어 초록 (Multilingual Abstract)

The metallic means are defined as the only positive real roots of x-1/x=n or x^2-nx=1. One of the most prominent applications of the metallic means is known as aperiodic tilings, such as the Penrose tiling or the Ammann-Beenker tiling. The Penrose tiling is already generalized to 3-dimensions as well. Another application of metallic means is on polyhedra : the golden ratio and silver ratio appear in various regular, Archimedean, and Catalan solids as well. This study categorizes previous studies on metallic means by the method of research, confirms whether the 3D Penrose tiling can be generalized to 4D figures, and verifies whether the golden ratio and silver ratio appear even in n-dimensional figures. As a result, it was revealed that the 4D Penrose tiling does not exist under certain conditions. Also, it was confirmed that the golden ratio and silver ratio could not appear in regular and semiregular polytopes in 5 dimensions or higher.

참고문헌 (Reference)

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