• Journal for History of Mathematics
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• v.19 no.2
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• pp.59-76
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• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• The Korean Publising Journal, Monthly
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• s.322
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• pp.6-7
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• 2002

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2005.11a
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• pp.9-9
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• 2005

• The Korean Publising Journal, Monthly
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• s.332
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• pp.110-111
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• 2003

• The Korean Publising Journal, Monthly
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• s.332
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• pp.112-113
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• 2003

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.31-42
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• 2005

Renaissance is revival of the ancient Greek and Roman cultures. So, in Renaissance period, the artists began to study Euclidean geometry and then their mind was a spirit of experience and observation. These spirits is namely modernism. In other words, Renaissance was a dawn of modern times. In this paper, we notice modern spirits and ones social backgrounds. Differential and integral calculus was created by these modern spirits. And in art field, 'painter of light', 'artist of moment' appeared. Because in the 17th and 18th centuries, the intelligentsia researched for motions, speeds and lights.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.59-68
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• 2003

Mathematics and arts are reflection of the spirit of the ages, since they have human inner parallel vision. Therefore, in ancient Greek ages, the artists' cannon was actually geometric ratio, golden section. However, in middle ages, the Euclidean Geometry was disappeared according to the Monastic Mathematics, then the art was divided two categories, one was holy Christian arts and the other was secular arts. In this research, we take notice of Renaissance Painting and Perspective Geometry, since Perspective Geometry was influenced by Renaissance notorious painter, Massccio, Leonardo and Raphael, etc. They drew and painted works by mathematical principles, at last, reformed the paradigm of arts. If we can say Euclidean Geometry is tactile geometry, the Perspective Geometry can be called by visual geometry.

• Archives of design research
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• v.12 no.1
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• pp.133-142
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• 1999

Light is an essential element which make it possible for men to see things, and its important for painter cannot be too much emphasized. light has significant meanings in the history of painting as well as in human life. light playa an essential role in creating three- dimentional objects. Light has not only spiritural, psychological , and formative meanings but also in. itself in the field of drawing. In general, a study of light and colors should be understood not merely as visible effects but as something unconscious involving psychological experiences and spiritual symbols, thus, as a very subjective phenomena. The article analyzes new meanings and roles of light in modern area, examining ways in which studies of light has been performed. It also deals with the meaning and effects of light revealed in the history of oriental and western paintings, and their influence on modern illustrations through case studies in order to provide an opportunity to have a new understanding of light.

• Archives of design research
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• v.12 no.3
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• pp.143-152
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• 1999

Although in art an idea which visualizes a certain concept is generally such an essential part as it would be decisive to the success or failure of an art work in reality various difficulties are involved in idea making. Thus, directions for the idea making for visualization works are suggested in this paper. This paper classifies several cases of expression skills among non-abstracts showing the contents which visualize abstract concepts in western art after Renaissance when freedom of individual artistic expression and personal characteristics initiated. Also, this paper selects and introduces art works in which expression skills can be obviously explained. The expression skills are divided into symbolizing, allegory, specific pattern, non-abstract skills of surrealism, metaphysical distortion of logic and situation fixing, and specific examples on how the abstract concepts are formed and delivered are described. This is a case study done for the purpose of supplying help for the idea making in the applied art field which is lack of this kind of study.