• 과학교육연구지
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• 제47권3호
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• pp.263-272
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• 2023

예비교사가 비유클리드 기하학에서 수학적 정의를 이용한 이차곡선의 학습으로 유클리드 기하학의 다양한 개념을 어떻게 이해하고 활용할 수 있는지를 살펴본다. 본 연구에서는 D 대학교 수학교육과 3학년 수업에서 수학적 정의를 이용하여 택시기하, 민코프스키 거리공간과 같은 비유클리드 공간의 이차곡선 학습이 예비교사들에게 새로운 기하학적 개념을 습득하고 수용하는 능력 향상에 도움을 줄 수 있음을 보였다. 이러한 결과로부터 택시기하와 민코프스키 거리공간에서의 정의를 활용한 이차곡선 학습이 창의적이고 유연한 사고를 유도하여, 예비교사들의 유클리드 기하학 교육 전문성 향상에 기여할 것으로 기대된다.

• 호남수학학술지
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• 제34권1호
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.537-554
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• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• 한국수학사학회지
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• 제24권4호
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• pp.21-31
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• 2011

이 글의 목적은 비유클리기하의 제안자의 한사람인 로바체프스키의 수학철학이 현대수학철학의 일종의 저수지였음을 보이고, 그의 수학철학이 비유클리드기하의 탄생에 기여했음을 밝히는 것이다.

• 한국통신학회논문지
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• 제29권5C호
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• pp.611-617
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• 2004

The optimum convolutional error correction codes for recently standardized Feher-patented quadrature phase-shift keying (FQPSK-B) modulation are proposed. We utilize the continuous phase modulation characteristics of FQPSK-B signals for calculating the minimum Euclidean distance of convolutional coded FQPSK-B signal. It is shown that the Euclidean distance between two FQPSK-B signals is proportional to the Hamming distance between two binary data sequence. Utilizing this characteristic, we show that the convolutional codes with optimum free Hamming distance is the optimum convolutional codes for FQPSK-B signals.

• 호남수학학술지
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• 제30권4호
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• pp.637-644
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• 2008

In this paper, we study some properties about the parallel surfaces of ruled surfaces in a Euclidean 3-space. Furthermore, we classify the parallel surfaces of ruled surfaces in a Euclidean 3-space satisfying a linear type and a quadric type with respect to the Gaussian curvature and the mean curvature.

• East Asian mathematical journal
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• 제31권5호
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• pp.677-684
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• 2015

In [7], it was shown that Euclidean rings R of imaginary quadratic integers admit unitary number systems. In this paper, as an application of the result, we obtain all self similar tiles arising from the unitary number systems of R.

• 한국수학사학회지
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• 제16권2호
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• pp.23-34
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• 2003

In this paper, we consider relationship between the mathematics and the fine arts. The former is one of the advanced sciences, the latter is one of the arts. But there is correlation between the mathematics and the arts. Here, we concern with the ancient greek mathematics, Euclidean geometry and the ancient greek arts. The ancient greek arts is classified with Geometric Style, Archaic Style, Classical Style and Hellenistic Style. The Geometric Style, Classical Style and Hellenistic Style are very effected by Euclidean geometry. Because the greek artists as keep the geometric proportion as the Euclidean's 5th postulates. The artist's cannon in just golden ratio 1:(1＋$\sqrt{5}$)/2.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.441-447
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• 2002

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.