• Honam Mathematical Journal
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• v.46 no.4
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• pp.587-605
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• 2024

We compute the zeta-determinants of the scalar Laplacians defined on the Möbius band and Klein bottle when the flat metrics are given. We consider the difference between these zeta-determinants and those of the product manifolds, and use the BFK-gluing formula to compute the difference. The zeta-determinants of product manifolds are well known and this computes the zeta-determinants on the Möbius band and Klein bottle. We finally show that the zeta-determinant on the Klein bottle satisfies the BFK-gluing formula.

• The Mathematical Education
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• v.38 no.1
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• pp.87-94
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• 1999

A multimedia CD title is developed for learning simple closed curve and Mobius band which are one of mathematics contents in the first grade of middle school. This title visualizes various figures through graphics and animations so that students can easily understand the relevant concepts and learn them with fun. It is shown that 88.6% of 30 sampled teachers are positive for the title and that 86.7% want to use it as a teaching tool in their classes.

• Korean Institute of Interior Design Journal
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• v.13 no.3
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• pp.69-75
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• 2004

Since 1990s, several rising western architects have been moving their theoretical background from the modern paradigm to new science and philosophy. Architectural spaces are based on the philosophy and science of their own age and the architectural theories made by them. And specially, it seems that topological spaces are different to theoretical backgrounds from idealized spaces of modern architecture. From these backgrounds, this study was performed to search for the spacial relationship and characteristics shown in the recently folding architecture and the results of this study that starts this purpose are as follows. First, the architecture that introduced by the theory of topology has appeared as the circulation forms like as Mobius band or Klein bottle, and was made the space fused with structure pursuing liquid properties of matter. As follows, second, the concept of topological space made the division of traditional concept of floor, wall, ceiling disappeared and had built up the space by continual transformation. Third, about the relationship between two spaces in topological space, the two spaces were happened by transformation of these and they have always continuity and the same quality.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1285-1325
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• 2011

We solve the isoperimetric problem, the least-perimeter way to enclose a given area, on various Euclidean, spherical, and hyperbolic surfaces, sometimes with cusps or free boundary. On hyperbolic genus-two surfaces, Adams and Morgan characterized the four possible types of isoperimetric regions. We prove that all four types actually occur and that on every hyperbolic genus-two surface, one of the isoperimetric regions must be an annulus. In a planar annulus bounded by two circles, we show that the leastperimeter way to enclose a given area is an arc against the outer boundary or a pair of spokes. We generalize this result to spherical and hyperbolic surfaces bounded by circles, horocycles, and other constant-curvature curves. In one case the solution alternates back and forth between two types, a phenomenon we have yet to see in the literature. We also examine non-orientable surfaces such as spherical M$\ddot{o}$obius bands and hyperbolic twisted chimney spaces.

• The Research Journal of the Costume Culture
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• v.10 no.6
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• pp.763-780
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• 2002

The aim of this research is to analyze Vionnet´s geometric features, which can be regarded as the key formative beauty among the external characteristics of her works. and to thereby establish the theory that her works emitted a time-transcending life force because they were patterns designed based on a geometrical frame of mind. To prove such argument, studies to understand the basic geometrical aspects appearing in her works will be made by taking a look at the general features of geometry, viewing Vionnet´s philosophy for designing, and examining the geometric cutting methods. The period covered in this paper will center mainly on dresses Vionnet made from her very active days in the fashion sector, 1919. till when she retired from the fashion industry, around 1939. What's outstanding about Vionnet´s geometric principle expressed in her works is the unique cutting method that acknowledges the silhouette of the human body as a cubic or three-dimensions concept, through insight of the human body, the mechanics of the materials, and geometry. Vionnet introduced a simple and elegant design by combining geometric figure cuts, such as rectan히es. quadrants, and triangles. Moreover, she created a new sewing structure that plans everything about the materials to the tiniest detail, resulting in producing a softer style With this, Vionnet showed the geometrical correlation can bring about harmony and the beauty of ideal proportion, forming the source of eternal beauty. As discussed so fu, the geometrical characteristics appearing in Vionnet´s works are marked such as spirals, zig-zag lines, asymmetries. panels, gradation, golden proportion, and the mobius-band.