• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• 대한수학교육학회지:학교수학
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• 제13권1호
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• pp.107-125
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• 2011

본 논문에서는 GSP(The Geometer's Sketchpad)를 이용한 역동적 기하 환경이 학생의 기하학적 성질의 추측에 어떤 영향을 미치는지를 살펴보았다. 좀 더 구체적으로 살피면, GSP 환경에서 학생들은 문제 상황에서 주어지지 않은 새로운 조건들을 생성하고 그 조건하에서 성질을 추측하는 활동이 활발하고, 문제의 조건이 너무 적은 개방적인 문제 상황에서는 추측 활동이 미약하였다. 또한 GSP 환경에서 추측한 성질은 지필환경에서 추측한 성질보다 복잡하였고 증명하기 어려웠으며 GSP의 다양한 기능 중 'Alt' 키를 이용하여 화면을 이동시킬 수 있는 기능은 측정과 계산 기능 등 과 같이 기하적 성질의 추측에 요긴하게 사용되었다. 또한 학생들은 기하적 성질을 증명할 때보다 스스로 기하적 성질을 발견하였을 때 더 자부심을 갖게 되며 더 기쁘게 생각하였다.

• Structural Monitoring and Maintenance
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• 제9권2호
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• pp.129-155
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• 2022

In this study, parametric analyses on a hoop-type PZT (lead-zirconate-titanate) interface are performed to estimate the effects of the PZT interface's materials and geometries on sensitivities of impedance responses under strand breakage. The paper provides a guideline for installing the PZT interface suitable in tendon anchorages for damage-sensitive impedance signatures. Firstly, the concept of the PZT interface-based impedance monitoring technique in prestressed tendon anchorage is briefly described. A FE (finite element) analysis is conducted on a multi-strands anchorage equipped with a hoop-type PZT interface for analyzing materials and geometric effects. Various material properties, geometric sizes of the interface, and PZT sensor are simulated under two states of prestressing force for acquiring impedance responses. Changes in impedance signals are statistically quantified to analyze the effect of these factors on damage-sensitive impedance monitoring in the tendon anchorage. Finally, experimental analyses are performed to demonstrate the effects of materials and geometrical properties of the PZT interface on damage-sensitive impedance monitoring.

• Korean Journal of Mathematics
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• 제21권3호
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• pp.223-236
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• 2013

Schensted algorithm was first described in 1938 by Robinson [5], in a paper dealing with an attempt to prove the correctness of the Littlewood-Richardson rule. Schensted [9] rediscovered Schensted algorithm independently in 1961 and Viennot [12] gave a geometric interpretation for Schensted algorithm in 1977. In this paper we describe some properties of Schensted algorithm using Viennot's geometric interpretation.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.135-141
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• 1997

In this paper, it is investigated the properties of the transformed geometric Poisson process when the intensity function of the process is a distribution of the continuous random variable. If the intensity function of the transformed geometric Poisson process is a Pareto distribution then the transformed geometric Poisson process is a strongly P-process.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권4호
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• pp.437-445
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• 2008

On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.

• East Asian mathematical journal
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• 제24권5호
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• 한국생산제조학회지
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• 제9권2호
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• pp.119-124
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• 2000

In this paper based on geometric optics and geometric modeling aspheric surface of the side mirror mold with dead angle reduced have been designed and machined in a CNC machining center, Surface roughness of the mold was evaluat-ed by usin the surface shaping system. Surface generating simulation of a ball endmill process is investigated. Through the simulation based on the surface-shaping system 3-D engineered surfaces and properties of engineered surfaces are obtained, Computer simulation provides the effective working conditions through the prediction of geometric properties of engineered surfaces. The rear view mirror and room mirror play important role on the safe driving condition as a observation of environment but the rear view mirror can not provide complete information of driving environments due to the existence of the dead angle. The analysis on the shape of formed mirror shows that the proposed me？ improves range of a driver's sight.

• International Journal of Reliability and Applications
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• 제9권1호
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• pp.31-52
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• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• 한국컴퓨터그래픽스학회논문지
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• 제7권1호
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• pp.19-25
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• 2001

본 논문에서는 평면 다항식 피타고리안 호도그라프 곡선을 그 근들의 관점에서 특별한 기하학적 재 매개화하는 것에 관하여 연구한다. 피타고라스 호도그라프 곡선들은 그 호도그라프의 근들에 의하여 완전히 결정된다. 피타고라스 호도그라프 곡선들의 근들의 자취는 아주 흥미로운 기하학적 성질들을 만족함을 보인다.