• 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.

• 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

• 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.10 no.2
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• pp.72-81
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• 1997

황금비는 이집트의 고왕국시대 혹은 더욱 그 이전으로 올라 갈 수가 있으나, 이 비율이 특히 고고학자나 미학자들 사이에서 학문적으로 중시 된 것은 르네상스 시대 이래의 현상이며, 황금비의 이름을 붙이게 된 것은 근세에 들어와서의 일이다. 이 황금비는 가장 조화가 잡힌 비로소 건축, 조각, 회화, 공예 등 조형예술의 분야에서는 다양한 통일의 하나의 원리로서 널리 활용되고 있다. 본고에서는 황금분할의 수학적 내용과 조형예술 분야에 미친 영향과 활용성을 살펴보았고, 그리고 황금비의 수리는 정연하고 신비적이기 때문에, 그것이 항상 아름답고 바람직할 것이라고 하는, 일종의 예측을 역사적으로 행해 왔던 젓임을 알 수 있었다.

• 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.

• 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 of Educational Research in Mathematics
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• v.27 no.3
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• pp.581-598
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• 2017

The early Renaissance artist Albrecht $D{\ddot{u}}rer$ is an amateur mathematician. He published a book on geometry. In the second part of that book, $D{\ddot{u}}rer$ gave compass and straight edge constructions for the regular polygons from the triangle to the 16-gon. For mathematics education, I extracted base constructions of polygon constructions. And I also showed how to use $D{\ddot{u}}rer^{\prime}s$ idea in constructing divergent forms with compass and ruler. The contents of this paper can be expected to be the baseline data for mathematics education.

• The Journal of the Convergence on Culture Technology
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• v.6 no.1
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• pp.255-261
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• 2020

Versatile and innovative interdisciplinary professionals refer to those who can engage in an efficient cooperation with experts in other fields or to those who can themselves put knowledge of different fields together. This article aims to look into Galileo Galilei as an example of historic figure that made remarkable achievements by merging knowledge in multiple fields of study. It also shows that Galileo, who had active exchange with painters during the Renaissance, presented the findings from his telescope observations in the form of drawings and that he used them to build core logics that criticizes the traditional Aristotelian cosmology. Galileo drew the critical logics, hardly achievable from a simple observation report or mathematical demonstration, from his hand drawing. The Galileo case well proposes the goals and direction of how the modern society should nurture its interdisciplinary professionals today.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.29 no.2
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• pp.90-98
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• 2011

This study aims to discuss the characteristics of garden architecture in Italian Renaissance Villa Lante that was constructed by the cardinal in Bagnaia at 16th century through actual survey and analysis of the garden's elements. To do this, it was studied in two ways: Analysis of the present conditions and review historical documents. The results are as follows. First, the buildings, the gardens and the surrounding landscapes are visually connected each other in relations between the topography and the surrounding landscapes. Second, the spatial composition accepted Neoplatonic law of multiple proportions and was influenced by ancient myth and "Liber ruralium commodorum" of Pietro de Crescenzi(1305). Third, the garden's elements consist of plants, buildings and items. In plants, the upper plants are fir tree, cypress and pine tree and the lower plants are english holly, box tree and sweet oleander. The buildings are casino, loggia and terrace. The items are pot, sundial, chair, viewing platform and fountain. The result of this study, the political and social, technical phenomena which constitute construction pattern affected the locational property and the spatial organization of the neighbor on Villa Lante.

• Anatomy & Biological Anthropology
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• v.29 no.2
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• pp.35-46
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• 2016

Leonardo da Vinci is remembered as the greatest genius of the Renaissance. He left outstanding achievements as an artist, scientist and inventor, and contributes up to today's science. He ranks the best in a variety of fields, such as botany, mathematics, geology, astronomy, geometry and optics. It has well known that Leonardo is an artist, scientist, inventor and philosopher. And he was a great anatomist that dissected dead bodies and animals directly and left many anatomical drawings. He took an interest in anatomy from the point of view of the artist, which is why the human body structure and function to know the sakes were "ignorant of the anatomy should not be upset." Over time, he became interested in the structure and function of the body, even get the human body in a difficult environment; he dissected many the human bodies directly. His scientific inquiry and infatuation made him as an advanced pioneer for more than 100 years, and got enough level to surpass the artistry. Leonardo left about 1,800 anatomical figures of the muscular, skeletal, vascular, nervous and urogenital system, and they are also very scientific and high artistic achievements. The aim of this article is to take a look at Leonardo da Vinci's anatomical achievements and thoughts. In addition, the goal is to knowledge today's anatomists about Leonardo da Vinci's astonishing achievements as a great pioneer in anatomy.