• 한국수학교육학회지시리즈A:수학교육
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• 제61권1호
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• pp.47-62
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• 2022

본 연구는 18세기 후반 조선산학서의 기하 영역 중 평면도형 관련 내용들이 이전 시기와 비교하여 어떻게 차별화되어 다루어졌는지 살펴보고, 평면도형과 관련된 설명과 계산법의 변화, 문제해결과정에서 수학적 논리의 엄밀성, 새롭게 등장한 수학 주제에 초점을 맞추어 분석하였다. 이를 위해 본 연구에서는 18세기 후반에 저술된 서명응의 <고사십이집>과 황윤석의 <산학입문>, 홍대용의 <주해수용>을 주 분석문헌으로 선정하여 이전시기의 <묵사집산법>, <구일집>과 비교하였다. 분석 결과, 도형을 측정 대상으로서가 아니라 성질을 탐구하는 대상으로 설명하고, 서법(西法)을 별해로 추가 제시하거나 기존 풀이법을 대체한 사례가 확인되었다. 또한 일부 문제에서 수학적 근거를 토대로 계산법의 타당성을 기술하거나 도형그림을 삽입한 도해(圖解)를 통한 설명, 근삿값에 대한 명확한 인식과 보다 정밀한 근삿값 설명 등은 수학적 논리의 엄밀성을 추구한 대표적 사례였다. 오늘날의 삼각함수에 해당하는 팔선(八線)과 삼각형의 구성요소 사이의 관계를 일반 삼각형으로 확장한 사례는 18세기 후반에 새롭게 등장한 기하 영역 주제였다. 이상은 18세기 후반의 조선산학이 서양수학의 이론적이고 논증적인 전개 양식을 점진적으로 수용한 근거라고 할 수 있다.

• 한국초등수학교육학회지
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• 제18권3호
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• pp.379-397
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• 2014

칸트에 의하면 인간은 현상을 시간의 틀 속에서 수용한다. 이로부터 시간적 현상의 무시간화와 무시간적 현상의 시간화라는 이해의 두 차원을 추출할 수 있다. 이 논문에서는 무시간적인 현상의 시간화와 시간적 현상의 무시간화가 수학적 지식 이해의 문제를 논하는 하나의 관점이 될 수 있음을 몇 가지 예를 들어 고찰한다. 먼저 무시간적 현상의 시간화의 의의를 수식과 도형을 예로 하여 고찰한다. 이어서 시간적 현상의 무시간화의 의의를 자연수의 합, 패턴, 확률 등을 예로 하여 고찰한다. 이러한 고찰을 바탕으로 수학교육에서 무시간적 현상을 시간화하여 이해하려는 성향과 시간적 현상을 무시간화하여 이해하려는 성향의 함양이 중요함을 논한다.

• 정보교육학회논문지
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• 제14권3호
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• pp.449-459
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• 2010

초등학교 도형 학습에 컴퓨터 프로그램을 활용하면 도형에 대한 다양한 조작 기능을 제공하여 학습의 효과를 높일 수 있으며, 탐구적 환경을 조성함으로써 교실 환경의 한계를 극복할 수 있다. 지금까지의 연구는 컴퓨터 프로그램을 활용한 도구들을 개발하였지만 콘텐츠 없이 도구이다. 본 연구는 Van Hieles의 기하 학습수준이론에 기초하여 초등학교 수학과 교육과정의 도형 영역을 분석하고, 초등학생들의 인지 수준에 적합한 도형 학습 문제 해결 도구(Geometry For Kids : GeoKids)를 개발한다. 학생들의 인지 수준을 고려하여 자와 컴퍼스를 대신할 수 있도록 만들었고, 원과 직선을 마우스를 사용하여 쉽게 그릴 수 있고, 보다 정확한 작도를 위하여 점과 원의 경계를 자동으로 인식하도록 구성하였다. 수학과 교육과정의 도형 학습 주제에 따라 GeoKids의 기능을 연계한 학습을 할 수 있다.

• 디자인학연구
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• 16호
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• pp.185-196
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• 1996

The series of ‘Dubonnet’poster is one of the masterpieces of Cassandre who was the leader of advertising poster in 1920's and 1930's. Orihinally it was a triptych, but it was developed as a serial work later through lettering and seasonal advertising posters. It was kept in circulation for more than two decades and issued in a variety of formats. In this thesis I tried to figure out the artistic character and uniqueness of Cassandre's poster by analyzing it with many different points of view of the poster, the stream of changing style and influence from the Avant-garde painting. In chapterII, objectively analyzing the series of‘Dubonnet’one by one, I examined the method that Cassandre used to deliver the concept of advertising and his message. The triptych, the first one of series of Dubonnet poster is witty, the slogan is a pun using the words dubo(doubt), bon(good), and Dubonnet, and the theme is treated as an animated sequence in the manner of a comic strip. In the following winter and summer seasonal advertising posters, the‘Dubonnet man’in the same position is enjoying the‘Dubonnet’, irrespective of the hazards of climate and season, There was a change towards 1929 that rectilinear design gave place to supple and undulating lines in Cassandre's posters. Seasonal advertising posters also showed the change, and the tendency of realistic and concrete elements of an expression was strengthened. In chapterIII, I studied three as main characters of Cassandre's poster. The first one is simple and geometric expression, second one is uniqueness of figures and the last one is important roll of lettering. Cassandre believed that there were fundamental differences between the function of a poster and that of a painting. He also recognized that the symbol was the essential element in the poster design, which would be simply and swiftly recognized. The recognition led him to simple design and bold geometric abstraction. He was a man who knew the value of copy in advertising and developed it fully in his simplified geometric compositions by integrating of letterforms and image. The‘Dubonnet man’is geometrized, almost featureless. This approach of rendering human beings was one that Cassandre had used from the early years, most notably in his posters for Dubonnet.

• 미술이론과 현장
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• 제3호
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• pp.173-192
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• 2005

Yoo Youngkuk started his career as an artist when he entered Bunkagakuin of Tokyo in 1935 he actively participated in the Japanese art scene as a young Korean artist until 1943. In his earliest works, Rhapsody and Work B, Surrealist and abstract influences are manifested as these were prevalent in Japan at the time. With the exception of Rhapsody and Work B, all works available that were executed between 1937 and 1940 are abstract, which points to the fact that Yoo intended abstraction from the beginning. Surviving works in relief suggest his early style was founded on the abstractions similar to Russian Avant-Garde, Neo-plasticism and Bauhaus simplicity. His early abstractions were not the ideational images derived in the process of the abstraction of the representational image, but they arose from the constructive attitude in composing the already stylized non-representational geometries. It is worth noting that his early emphasis was on the pure and absolute geometric abstraction, rather than the images motivated from the figurative representation. Yoo differentiates himself from Kim Whan Ki in the following aspects: one, he eliminated the subject matter i.e. human figures and the nature; two, he maintained the constructivist attitude in creating a strict and absolute abstraction; three, he experimented with different styles without combining them. He manifests direct influences from the prevalent Western art influences, such as Futurism and Russian Avant-Garde, unlike Kim who vaguely references. In both paintings and reliefs, Yoo's attempt in the realization of the pictorial depth and space seems cerebral and conceptualized compared with the other artists of the time who resolved abstraction via the constructive dimension. Uemura, a contemporary critic to the geometric abstractions in Japan, disapproves the stylistic bent in the adaptation of the abstract painting without the comprehension of its spiritual movement. As witnessed in other criticisms as well, contemporary Japanese critics' interest lie mainly in the superficial observation such as the presence of representational elements, composition and use of color. Such formal and superficial understanding of the geometric abstraction resulted in

• 충청수학회지
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• 제27권2호
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• pp.211-218
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• 2014

In 3-dimensional Euclidean space, the geometric figures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry. In this paper, we define parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curvature of the surface with curvature and torsion of the given curve. In particular, we find some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• East Asian mathematical journal
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• 제36권2호
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• pp.131-146
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• 2020

The isoperimetric problem is a well-known optimization problem from ancient Greek. Among plane figures with the same perimeter, which is the largest area surrounded? The answer to the question is circle. Zenodorus and Steiner's pure geometric proofs, which left a lot of achievements in this matter, looked beautiful with ideas at that time. But there was a fatal flaw in the proof. The weakness is related to the existence of the solution. In this paper, from a view of the existence of the solution, we investigate proofs of Zenodorus and Steiner and get educational implications.

• 대한수학교육학회지:학교수학
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• 제15권2호
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• pp.481-501
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• 2013

본 연구는 역동기하 환경에서 "끌기"의 역할을 고찰하고자 한다. 끌기는 도형을 역동적으로 변화시키면서 기하 도형의 숨겨진 성질과 이들 사이의 관계를 나타내는 불변성을 탐색 가능하게 하는 중요한 역할을 한다. 따라서 본 연구는 선행 연구의 분석을 통해 역동기하 환경에서 끌기의 사용이 세 가지 관점으로, 즉 역동적 표상, 도구유발행위, 그리고 어포던스로 구분될 수 있다는 결론을 도출하였다. 본 연구에서는 끌기의 사용에 대한 이들 각각의 관점을 선행 연구를 중심으로 살펴보았다. 그리고 이로부터 (1) 연역적, 공리적, 형식적 지필기하를 실험수학으로 접근할 수 있게 하는 끌기의 가능성 탐구, (2) 추측과 증명 사이에서 끌기의 유형에 따른 작용 분석, (3) 학생과 DGS 사이의 도구발생 과정에 따른 기하 학습의 차이 분석, (4) 끌기에 의한 의사소통이나 담화 유형의 분석, (5) 어포던스로서 끌기에 의해 수반되는 측정 기능의 역할 분석, 그리고 (6) 끌기에 의한 기하 개념의 정의에 대한 학생들의 인식론적 변화를 기하의 교수-학습과 후속연구를 위한 제언으로 제시하고 있다.

• 한국의류학회지
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• 제36권7호
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• pp.727-740
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• 2012

This study is for the enhancement and utilization of future graphic design for T-shirts and deals with the expression styles and features of T-shirt graphic designs that appear in modern fashion. A literature examination about graphic design and T-shirts was performed for the research method and the analysis followed 378 pieces of graphic design featured in four major international collections for females from 2001S/S to 2011S/S. The research results from the expression type of T-shirt graphic design in the modern fashion are as follows. Expression in graphic figure accounts for the largest portion of 40.8% that includes illustration or cartoon characters, personal figure or part of the physical body, object in daily life or landscape pictures, animals and plants, and others. Expression given in text with typography or logo accounted for 27.5%, expression combined with letter/text, graphics and geometric figures accounted for 24.3%, geometrical expression accounted for 7.4%; most of which are given in print. Characteristics found in modern fashion graphic design are as follows. First, role of sort of public relations marketing was accompanied with utilization of brand logo or symbol. Second, visual play was shown in a sense of humor with diverse graphic figures and playful texts, witty layout with graphic motives, and a free design formation. Third, it denoted a front burner issue delivering the message for various current events or arguments via the way of texts, slogans, and symbolic pictures. Fourth, it depicted artistry through the self-expressive creation of the designer.