• Proceedings of the Korea Society of Design Studies Conference
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• 2001.05a
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• pp.146-147
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• 2001

• Korean Institute of Interior Design Journal
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• v.17 no.5
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• pp.40-50
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• 2008

This article examined the applicability of spatial configuration to Escher's works through configurative logics and rules and studied the contrasting relations among the unit elements in Escher's works and their characteristics and the creative process of the characteristics. As the results of the study on the bases to maintain and create the partial elements revealed as the characteristics, it was shown that Escher's sequential transformative works demonstrated diverse expressive characteristics as a creative process of Inter-complementary contrasting relations based on the independence of the unit elements. It was also shown that the creative process of the unit elements was actualized through the maintenance base of the fixed and absolute characteristic as the logic for the creation and the creation base of the dynamic and relative characteristic. Therefore, it was interpreted that by applying the logics for creation to Escher's unit elements through the spatial interpretation of the maintenance base and the creation base as well as by configuring the units created in such a way according to the characteristics of Escher's works, spatial possibility canbe derived out from Escher's contrasting tessellation works. The process of spatial configuration is the process to make a balance between various conditions, artists own understanding of the space and his/her intention of the space. From this viewpoint, the logics for maintenance base and for creation base seem to have the potentiality as a spatial configuration to consistently meet the given conditions as well as to derive out novelty through the transformation to maintain the fixed and absolute condition(base) and the characteristics of the independent(additional) transformation arising together with the implicit relations among the transformative units.

• Archives of design research
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• v.15 no.1
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• pp.5-14
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• 2002

Fractal which was named by Mandelbrot in 1975 and its theory have been taken notice of many fields of scholarship, namely mathematics, physics, geography, architecture, art, philosophy and so on. If we approach Fractal on the basis of the designing cogitation, it can be used not only as one of materials to take a crease thinking in design, also as a due of the methods to assess the design problem with a new point of view. Based on above background, in this study, it was studied on the graphic artist, Morits Collelius Escher who has been well known as the great artist of illusion," and on the attributes of Fractal which were contained in his various work\ulcorner As a reset, the four attributes, namey ′fractal dimension′, ′self-similarity, ′recursiveness′and ′infinity were founded in his works. Also, it was founded that Escher had employed the attributes of Fractal in his almost works for "the representation of the condition of unified-duality," that is to say, for the union of two different dimensions. After this, it is expected that this study shoed be extended to the development of the principle of Fractal-Design on the basis of ′Fractal which can be defined as the phenomenon of repetitious pattern between chaos and order and′the formative beauty of Fractal′.

• Korean Institute of Interior Design Journal
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• no.39
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• pp.12-19
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• 2003

M.C Escher was not a mathematician or architect, but a visual graphic woodblock artist. He expresses space in various angles such as illusion and space not represented in reality, repetition, geometric pattern and change in space vision. However, as his works represent the impossible space which is virtually not exist in reality, they were examined numerically by scientists and mathematicians rather than by designers. Because his distinctive approach to view space, his works have been highly evaluated by scholars in various fields. Based on the previous research by mathematicians and scientists, this study will examine the sp- atial logic was represented visually in the works of M.C Escher and find out the possible and adoptable alternatives for new space design and provide the design application direction in the expression of interior space.

• The Journal of the Korea Contents Association
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• v.9 no.7
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• pp.102-109
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• 2009

In this paper, we present an algorithm which generates the impossible drawings after the manner of M.C. Escher. A class of the impossible drawings, focused on this paper, depicts the non-realistic configuration such that an ascent (or a descent) looks like keeping on permanently with a height-deceptive loop. We analyze the fact that the ascending direction in the non-realistic illustrations comes not from the physical heights of the objects but from the artist's intended forwarding direction about the loop, which does not have any physical sense of depths. The basic idea to support such impossible drawings is to use a loop of layered depth images (LDIs), where several LDIs are arranged along with the forwarding direction of the loop while having the physically constant heights. The height-deception between two adjacent objects comes from the layer values in the LDIs. In this paper, we propose a NPR system which can manipulate a shape of the loop and layer values of the LDIs and demonstrate several impossible drawings results generated by using our system.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.275-284
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• 2005

Tessellations are the pattern of iterations of geometric symmetry and translation. We can find them in the works of Escher who is the famous Dutch artist, and the American Indean life. Also, we can find the beauty of tessellations in the Korean traditional house door, Buddist temple architecture, palace's fence, etc. In the article, the figures of patterns we present are bird, fish, cat, pig, elephant, penguin, child and horse riding man, including Escher's, which are constructed using the computer geometric program, GSP (Geometer's Sketchpad). We want to talk about girl's disposition toward mathematics related to the figures. If they are supported by this kind of interesting figures constructed by their own hands, students will have more interest in learning geometric figures.

• The Journal of the Korea Contents Association
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• v.10 no.4
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• pp.447-457
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• 2010

Mathematical principle is present in artwork or architectural building. It is important for middle school students to find these mathematical principles in artwork. But it is difficult to achieve original purpose of art education through student activity that only looks for mathematical principle present in artwork and architectural building. Thus, it is necessary for students to have activities to find mathematical principle in artwork for themselves through artistic experience and appreciation of artwork and to create, appreciate and express new artwork to which they apply the mathematical principle. In this article, I researched a couple of artwork or architectural buildings from this point of view in which mathematical principle is present. I also developed hypothetical teacher activities and student activities for program by providing artwork of Escher in which mathematical principle is present as an example.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.1-11
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• 2001

The purpose of the study is to introduce how tessellation can be used and integrated to connect geometry to pattern in elementary mathematics educations. Tessellation examples include transformations such as translational symmetry, rotational symmetry, reflection symmetry, and glide reflection symmetry. In addition, many examples of tessellation using softwares such as Escher, TesselMania!, and LOGO programs. Further, future study will continue to foster students and teachers to try to construct their alive mathematics knowledge. The study of geometry and patterns require a rich teaching and learning environment provided by in-depth understanding of thinking connections to objects in real world.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.539-556
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• 2006

Tessellations are the pattern of iterations of geometric transformation. We can find them in the works of Escher, the famous Dutch artist. Also, We can find the beauty of tessellations in traditional Korean house doors, old Korean architecture, palace walls, and so forth. In this article, the figures of patterns we present are a pig, a frog, Tchiucheonwhang (the mascot of Korean football supporters), and figures by Escher, using the computer geometric program, GSP (Geometer's Sketchpad). We wanted to investigate the gender differences on students' achievement and disposition toward mathematics in constructing tessellations. The results indicated that if students were supported with well prepared instructional materials which helped students make their own figures, female students in particular would be more interested in learning geometric transformation.

• Proceedings of the SCSK Conference
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• 1999.10a
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• pp.17-41
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• 1999

Manuka oil sometime named New Zealand's tea tree oil is soluble in oil and come from nature. The $\alpha$-pinene extracted from Manuka oil and R-limonene which is one of the component of extracted Citrex from Grapefruit were used to estimate the antimicrobial activity and to improve the capability of antiseptic. Disk diffusion and broth dilution methods were used to measure the antimicrobial activity Escherichia coli which is gram-negative bacteria and Staphylococcus aureus which is gram-positive bacteria were used as strain. The antimicrobial activity of Manuka oil and $\alpha$-pinene for Escherichia coli, Staphylococcus aureus is similar when the concentration of Manuka oil and $\alpha$-pinene is 10${mu}ell$. However, Antimicrobial activity of Manuka oil for EscherEchta coli, Staphylococcus aureus is better than that of $\alpha$-pinene when the concentration of Manuka oil and $\alpha$-pinene is low. Antimicrobial activity of Citrex is superior to that of R-limonene. The proper ratio of Maunka oil and Citrex can Improve the antimicrobial activity. The proper ratio obtained from studies was 75% of Maunka oil and 25% Citrex for Escherichia coli, 25% of Maunka oil and 75% Citrex for Staphylococcus aureus.