• Title/Summary/Keyword: infinite concepts

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Mathematical Infinite Concepts in Arts (미술에 표현된 수학의 무한사상)

  • Kye, Young-Hee
    • 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.

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OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS

  • Jaiswal, Monika;Mishra, Shashi Kant;Al Shamary, Bader
    • Communications of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.411-423
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    • 2012
  • A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.

Philosophical Thinking in Mathematics (수학의 철학적 사유)

  • 김용운
    • Journal for History of Mathematics
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    • v.1 no.1
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    • pp.14-32
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    • 1984
  • The concepts of zero, minus, infinite, ideal point, etc. are not real existence, but are pure mathematical objects. These entities become mathematical objects through the process of a philosophical filtering. In this paper, the writer explores the relation between natural conditions of different cultures and philosophies, with its reference to fundamental philosophies and traditional mathematical patterns in major cultural zones. The main items treated in this paper are as follows: 1. Greek ontology and Euclidean geometry. 2. Chinese agnosticism and the concept of minus in the equations. 3. Transcendence in Hebrews and the concept of infinite in modern analysis. 4. The empty and zero in India.

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A Study on the instruction of the Infinity Concept with suitable examples - focused on Curriculum of Middle School - (무한 개념의 지도방안과 활용 예제 - 중학교 교육과정을 중심으로 -)

  • Kim, Mee-Kwang
    • The Mathematical Education
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    • v.47 no.4
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    • pp.447-465
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    • 2008
  • The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

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A Historical Study on the Interaction of the Limit-the Infinite Set and Its Educational Implications (극한과 무한집합의 상호작용과 그 교육적 시사점에 대한 역사적 연구)

  • Park, Sun-Yong
    • Journal for History of Mathematics
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    • v.31 no.2
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    • pp.73-91
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    • 2018
  • This study begins with the awareness of problem that the education of mathematics teachers has failed to link the limit and the infinite set conceptually. Thus, this study analyzes the historical and reciprocal development of the limit and the infinite set, and discusses how to improve the education of these concepts and their relation based on the outcome of this analysis. The results of the study confirm that the infinite set is the historical tool of linking the limit and the real numbers. Also, the result shows that the premise of 'the component of the straight line is a point.' had the fundamental role in the construction of the real numbers as an arithmetical continuum and that the moral certainty of this premise would be obtained through a thought experiment using an infinite set. Based on these findings, several proposals have been made regarding the teacher education of awakening someone to the fact that 'the theoretical foundation of the limit is the real numbers, and it is required to introduce an infinite set for dealing with the real numbers.' in this study. In particular, by presenting one method of constructing the real numbers as an arithmetical continuum based on a thought experiment about the component of the straight line, this study opens up the possibility of an education that could get the limit values psychologically connected to the infinite set in overcoming the epistemological obstacle related to the continuum concept.

Concept Images and Definitions of Conepts of Infinity and Limits for High School Students (고등학생의 무한에 대한 개념정의와 개념이미지)

  • Whang, Woo-Hyung;Jee, Young-Jo
    • Journal of the Korean School Mathematics Society
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    • v.11 no.2
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    • pp.249-283
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    • 2008
  • The purpose of the study was to investigate the definitions and concept images of Infinity and limits for high school students. In addition, the error patterns of the students were also investigated. The participants were 121 girls highschool students and survey method was used to co11ed data. Only 11 % and 5% of the participants revealed the definitions similar to the standard textbook definitions in limits of infinite sequences and infinite series respectively. The participants showed 6 types of error patterns and had more difficulties in understanding and applying concepts and properties of infinite series than those of infinite sequences.

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Efficient analysis of SSI problems using infinite elements and wavelet theory

  • Bagheripour, Mohamad Hossein;Rahgozar, Reza;Malekinejad, Mohsen
    • Geomechanics and Engineering
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    • v.2 no.4
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    • pp.229-252
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    • 2010
  • In this paper, Soil-Structure Interaction (SSI) effect is investigated using a new and integrated approach. Faster solution of time dependant differential equation of motion is achieved using numerical representation of wavelet theory while dynamic Infinite Elements (IFE) concept is utilized to effectively model the unbounded soil domain. Combination of the wavelet theory with IFE concept lead to a robust, efficient and integrated technique for the solution of complex problems. A direct method for soil-structure interaction analysis in a two dimensional medium is also presented in time domain using the frequency dependent transformation matrix. This matrix which represents the far field region is constructed by assembling stiffness matrices of the frequency dependant infinite elements. It maps the problem into the time domain where the equations of motion are to be solved. Accuracy of results obtained in this study is compared to those obtained by other SSI analysis techniques. It is shown that the solution procedure discussed in this paper is reliable, efficient and less time consuming as compared to other existing concepts and procedures.

Architectural Manifestation of Hiroshi Sugimoto's Photographic Infinity (히로시 스기모토의 사진작품에 드러나는 무한성의 건축적 발현에 대한 연구)

  • Ahn, Seongmo
    • Korean Institute of Interior Design Journal
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    • v.24 no.5
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    • pp.31-41
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    • 2015
  • The objective of this research is to investigate the artistic meaning of "infinity," manifested by the fourth dimensional value in the genres of photography and architecture, by analyzing how Sugimoto Hiroshi's photographic spatio-temporal infinity transfers to his architectural approaches. The research is initiated by scrutinizing the themes, characteristics, techniques, and artistic meaning of Sugimoto's famous photographic series, including "Seascapes," "Theatres," and "Architecture"; the concept of infinity can be defined as infinite divergence and infinitesimal convergence between antithetical concepts in time, space, and being. Sugimoto's photographic works display "temporal infinity" by connecting ancient times, the present, and the future; "spatial infinity" by offering the potential for transformation from flat photographs into infinite three-dimensional space and fourth-dimensional concepts through time; and "existential infinity" of life and death by making us think about being and essence, being and time, and origin and religion. These perspectives are also used to analyze Sugimoto's architectural works, such as "Appropriate Proportion" and "Glass Tea House Mondrian." As a result, the research finds that in Sugimoto's architectural approaches, spatio-temporal infinity between antithetical values is manifested through the concept of origin, geometric form, extended axis, immaterial threshold, transparent materiality, and connectivity of light and shadow, provoking our existence to transcend into infinity itself.

Bolzano and the Evolution of the Concept of Infinity (무한 개념의 진화 : Bolzano를 중심으로)

  • Cheong, Kye-Seop
    • Journal for History of Mathematics
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    • v.21 no.3
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    • pp.31-52
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    • 2008
  • The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.

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An Analysis on Effects of Phase Compensation on Power System Stability in the PSS Parameter Tuning (PSS Tuning시 위상보상이 계통안정도에 미치는 영향 분석)

  • Kim, Tae-Kyun;Shin, Jeong-Hoon
    • Proceedings of the KIEE Conference
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    • 1998.07c
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    • pp.1147-1149
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    • 1998
  • This paper presents the result of an analysis on effects of phase compensation on power system stability in the PSS parameter tuning. Synchronizing and damping coefficients are induced from lineal model for generator with PSS. Synchronizing and damping coefficients corresponding to time constants of phase compensation control block are calculated on a single machine, infinite bus test system. The Parameter tuning concepts, basic function, structural elements and performance criteria of PSS are introduced.

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