• The Mathematical Education
• /
• v.61 no.1
• /
• pp.47-62
• /
• 2022

This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

• Journal of Elementary Mathematics Education in Korea
• /
• v.18 no.3
• /
• pp.379-397
• /
• 2014

According to Kant, time is integral to all human cognitive experiences. Human beings perceive things in the frame of time. Phenomena are perceived in successive way or in coexistent way. In this paper, I argue that the perspective of temporality and atemporality can be a framework to consider the issues of teaching and understanding of mathematical knowledge. Significance of temporal inquiry of atemporal phenomena is discussed with examples of mathematical expressions and geometric figures. Significance of atemporal inquiry of temporal phenomena is also discussed with examples of the sum of natural numbers, geometric pattern, and the probability of two events. Teachers should understand the potential of mathematical tasks from the perspective of temporality and atemporality and provide students with opportunities to inquire temporal phenomena atemporally and atemporal phenomena temporally.

• Journal of The Korean Association of Information Education
• /
• v.14 no.3
• /
• pp.449-459
• /
• 2010

Using a geometric computer program achieve learning effects as handling various function and has advantage to overcome the environment of classroom through providing an inquiring surroundings in the figure learning at an elementary school. There are many software for drawing the geometric. But currently most is focus on how to use the softwares without contents. So, It is necessary to develope a geometric software adapted cognitive development of primary schoolchildren. This study is aim to analyze elementary mathematic curriculum based on Van Heiles theory, to develope the software(Geometry for Kids : GeoKids) considering cognitive level of the primary schoolchildren. This software is developed to substitute a ruler and a compass considering cognitive level of the primary schoolchildren. Using mouse, GeoKids software help a child to draw easily lines and circles and this software notice another lines and circle automatically for a more accurate drawing figures. Children can use practically this software in connection with subjects of elementary mathematic curriculum.

• Archives of design research
• /
• no.16
• /
• pp.185-196
• /
• 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.

• The Journal of Art Theory & Practice
• /
• no.3
• /
• pp.173-192
• /
• 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

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.2
• /
• pp.211-218
• /
• 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
• /
• v.10 no.1_2
• /
• pp.245-250
• /
• 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
• /
• v.36 no.2
• /
• pp.131-146
• /
• 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.

• School Mathematics
• /
• v.15 no.2
• /
• pp.481-501
• /
• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of the Korean Society of Clothing and Textiles
• /
• v.36 no.7
• /
• pp.727-740
• /
• 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.