• 한국수학교육학회지시리즈E:수학교육논문집
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• 제31권2호
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• pp.103-121
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• 2017

택시기하는 수학 영재를 위한 기하 영역의 학습 자료를 개발함에 있어 사용되는 대표적인 비유클리드 기하학이다. 택시기하에서 이차곡선과 관련된 수학 영재 프로그램은 기하대수적 정의에 따른 이차곡선의 탐구만 이루어져 있었다. 이에 본 연구에서는 유클리드 기하의 3가지 정의 방법(기하대수적 정의, 이심률 정의, 원뿔곡선의 정의)을 택시기하에서 적용시켜 나타난 이차곡선 그래프의 개형을 살펴보았다.

• Structural Engineering and Mechanics
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• 제83권1호
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• pp.1-17
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• 2022

The static design approach in the current code implies that the inherent torsional moment represents the state of zero inertial torsional moments at the center of mass (CM). However, both experimental and analytical results prove the existence of a large amount of the inertial torsional moment at the CM. Also, the definition of eccentricity by engineers, which is referred to as the resistance eccentricity, is defined as the distance between the center of mass and the center of resistance, which is conceptually different from the static eccentricity in the current codes, defined as the arm length about the center of rotation. The difference in the definitions of eccentricity should be made clear to avoid confusion about the torsion design. This study proposed prediction equations as a function of resistance eccentricity based on a resistance eccentricity model with advantages of (1) the recognition of the existence of torsional moment at the CM, (2) the avoidance of the confusion by using resistance eccentricity instead of the design eccentricity, and (3) a clear relationship of applied inertial forces at the CM and resisting forces. These predictions are compared with the seismic responses obtained from time-history analyses of a five-story building structure under moderate and severe earthquakes. Then, the trend of the resistance eccentricity corresponding to the maximum edge drift is investigated for elastic and inelastic responses. The comparison given in this study shows that these prediction equations can serve as a useful reference for the prediction in both the elastic and the inelastic ranges.

• Earthquakes and Structures
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• 제19권1호
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• pp.59-77
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• 2020

The code static eccentricity model for elastic torsional design of structures has two critical shortcomings: (1) the negation of the inertial torsional moment at the center of mass (CM), particularly for torsionally-unbalanced (TU) building structures, and (2) the confusion caused by the discrepancy in the definition of the design eccentricity in codes and the resistance eccentricity commonly used by engineers such as in FEMA454. To overcome these shortcomings, using the resistance eccentricity model that can accommodate the inertial torsional moment at the CM, interactive relations between shear and torsion are proposed as follows: (1) elastic responses of structures at instants of peak edge-frame drifts are given as functions of resistance eccentricity, and (2) elastic hysteretic relationships between shear and torsion in forces and deformations are bounded by ellipsoids constructed using two adjacent dominant modes. Comparison of demands estimated using these two interactive relations with those from shake-table tests of two TU building structures (a 1:5-scale five-story reinforced concrete (RC) building model and a 1:12-scale 17-story RC building model) under the service level earthquake (SLE) show that these relations match experimental results of models reasonably well. Concepts proposed in this study enable engineers to not only visualize the overall picture of torsional behavior including the relationship between shear and torsion with the range of forces and deformations, but also pinpoint easily the information about critical responses of structures such as the maximum edge-frame drifts and the corresponding shear force and torsion moment with the eccentricity.

• 대한수학교육학회지:학교수학
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• 제15권4호
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• pp.995-1013
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• 2013

본 연구의 목적은 현직교사의 이차곡선 영역 수학내용 지식의 이해 정도를 조사하는 데 있다. 이를 위해 수학교사에게 필요한 수학 내용 지식을 학교수학의 내용지식과 과정지식, 학교수학과 연결된 학문적 수학으로 구분하고, 이를 교육과정과 연결하여 검사지를 개발하였다. 연구대상은 수학과 심화연수에 참여한 현직교사 24명이었으며, 연구결과 현직 수학교사들은 타원과 쌍곡선의 원뿔곡선의 정의와 이심률 정의에 대한 인지도가 낮았으며, 특히 이심률에 의한 정의를 쓴 교사는 1명도 없었다. 그리고 단델린 공을 이용한 원추곡선 정의와 이차곡선 정의의 동치관계를 설명하는 것을 어려워했다. 또한 타원과 쌍곡선의 접선 작도 문제에 대해서는 접선작도법 자체에 대한 문제보다 접선을 이용한 응용원리를 묻는 문제에 대해 옳게 반응한 비율이 높은 것으로 나타났다. 이러한 연구결과는 교사교육 프로그램에서 수학 내용 지식에 대한 학습 기회를 충분히 제공할 필요가 있음을 시사한다.

• 영미문화
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• 제10권2호
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• pp.209-230
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• 2010

This paper reads Tristram Shandy around the issue of hobbyhorse, Sterne's main contribution to novelistic techniques as well as his insightful understanding of the modern condition. First, Sterne represents his characters according to the principle of hobbyhorse, declaring "I will draw my uncle Toby's character from his HOBBY-HORSE." Gradually distancing himself from the Juvenalian satiric mode as well as Henry Fielding's grand narrative and Samuel Richardson's psychological realism, as is seen in the early episode of Yorick's death, Sterne suggests that the best way to represent his characters lies in describing their hobbyhorses. Sterne's foregrounding of hobbyhorse is linked with his embrace of madness as part of the modern identity. He accepts that hobbyhorse-riding, a quirky and mad habit of mind or behavior, is indispensable for some people, like Uncle Toby, to survive and get along with their otherwise unbearable lives. Uncle Toby's hobbyhorse of waging mock battles in the bowling green saves him from the perplexing real world of language and sexuality, while the fictionality of his hobbyhorsical world is exposed by Widow Wadman. Since a hobbyhorse is by definition a world of private pleasure and eccentricity, sentimentalism comes along to bridge the two virtually incommensurable hobbyhorsical world in place of linguistic communication. Yet if Tristram Shandy fully stages sentimentalism, a cardinal part of hobbyhorse riding, it also offers an awareness of it, which is a significant development in the cult of sentimentalism in the eighteenth century. Tristram Shandy performs a version of sentimental journey where each character rides his hobbyhorse and the reader is invited to ride his/her own hobbyhorse.