• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.119-139
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• 2017

The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.

• Journal for History of Mathematics
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• v.33 no.1
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• pp.33-53
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• 2020

Euclid's Elements has been considered as the stereotype of logical and deductive approach to mathematics in the history of mathematics. Nonetheless, it has been criticized by its dryness and difficulties for learning. It is worthwhile to noticing mathematicians' struggle for providing some alternatives to Euclid's Elements. One of these alternatives was written by a French scientist, Pardies who called it 'Elemens de Geometrie ou par une methode courte & aisee l'on peut apprendre ce qu'il faut scavoir d'Euclide, d'Archimede, d'Apllonius & les plus belles inventions des anciens & des nouveaux Geometres.' A precedent research presented its historical meaning in traditional mathematics of China and Joseon as well as its didactical meaning in mathematics education with the overview of this book. However, it has a limitation that there isn't elaborate comparison between Euclid's and Pardies'in the aspects of contents as well as the approaching method. This evokes the curiosity enough to encourage this research. So, this research aims to compare Pardies' Elements and Euclid's Elements. Which propositions Pardies selected from Euclid's Elements? How were they restructured in Pardies' Elements? Responding these questions, the researcher confirmed his easy method of learning geometry intended by Pardies.

• Journal for History of Mathematics
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• v.34 no.1
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• pp.1-20
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• 2021

Logic and intuition are considered as the opposite extremes of teaching geometry, and any teaching method of geometry is to be placed between these extremes. The purpose of this study is to identify the characteristics of logical and intuitive approaches for teaching geometry and to derive didactical implications by taking Euclid's Elements and Clairaut's Elements respectively representing the extremes. To this end, comparing the composition and contents of each book, we analyze which propositions Clairaut chose from Euclid's Elements, how their approaches differ in definitions, proofs, and geometrical constructions, and what unique approaches Clairaut took. The results reveal that Clairaut mainly chose propositions from Euclid's books 1, 3, 6, 11, and 12 to provide the contexts that show why such ideas were needed, rather than the sudden appearance of abstract and formal propositions, and omitted or modified the process of justification according to learners' levels. These propose a variety of intuitive strategies in line with trends of teaching geometry towards emphasis on conceptual understanding and different levels of justification. Specifically, such as the general principle of similarity and the infinite geometric approach shown in Clairaut's Elements, we could confirm that intuition-based geometry does not necessarily aim for tasks with low cognitive demand, but must be taught in a way that learners can understand.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.285-288
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• 2000

In this paper, we propose a Reed-Solomon decoder for the DVD Reed-Solomon(RS) product code based on new efficient euclid cell architecture suitable for Modified Euclid Algorithm. We synthesized the RS decoder using Hyundai 0.65um CMOS standard cell library and compared the performance of the decoder with one of the conventional architectures. The result shows that the proposed euclid cell use about 32% less symbol time.

• The Mathematical Education
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• v.15 no.1
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• pp.5-7
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• 1976

Euclid 기하학이 성립하는 공간은 우리들과 가장 밀접한 공간이다. Descartes의 해석기하학은 Euclid의 3차원공간에서 성립한다. 이 경우 점이라 해도 그것은 3개의 실수의 순서쌍(x, y, z)에 의해 표현되는 것으로 생각해도 좋다. 일반의 n차원 Euclid 공간 R$^n$에 대해서도 같은 생각으로 정의할 수 있다. 이 경우 n=1은 수치선, n=2는 평면, n=3은 소위 3차원의 공간으로서 직관적으로 상상할 수 있으나 n(equation omitted)4인 경우는 상상하기 어렵다. 여기서는 거리의 성질과 추상공간을 논하고 Euclid 공간의 거리에서 출발하여 그 성질중 삼각부등식을 계산을 통하여 증명하므로서 공간의 확장화가 이루워짐을 보였다.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.45-56
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• 2003

In this paper, we investigate the origin of Euclid's fifth postulate. For this we analyze the Euclid's proof of the Pythagorean theorem, so form a hypothesis "The Euclid's fifth postulate originated from the Pythagorean theorem." And we test our hypothesis by some historical evidences.evidences.

• School Mathematics
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• v.4 no.3
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• pp.347-360
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• 2002

This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.6
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• pp.37-43
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• 1999

Two-way addressing method has been proposed for efficient VLSI implementation of Euclidean calculation circuit for pipelined Reed-Solomon decoder. This new circuit is operating with single clock while exploiting maximum parallelism, and uses register addressing instead of register shifting to minimize the switching power. Logic synthesis shows the circuit with the new scheme takes 3,000 logic gates, which is about 40% reduction from the previous 5,000 gate implementation. Computer simulation also shows the power consumption is about 3mW. The previous implementation with multiple clock consumed about 5mW.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.31-46
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• 2011

[ ${\ll}$ ]n divisions of figures(${\pi}{\varepsilon}{\rho}{\acute{\iota}}\;{\delta}{\iota}{\alpha}{\iota}{\rho}{\acute{\varepsilon}}{\sigma}{\varepsilon}{\omega}{\nu}\;{\beta}{\iota}{\beta}{\lambda}{\acute{\iota}}o{\nu}$)${\gg}$ is one of the works written by Euclid, but little known to us. In this paper, we introduce this Euclid's book on divisions of figures with its brief history, analyse its contents, and discuss how to use it in mathematics education.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.8A
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• pp.820-826
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• 2007

This paper proposes an enhanced degree computationless modified Euclid's(E-DCME) algorithm and its architecture for Reed-Solomon decoders. The proposed E-DCME algorithm has shorter critical path delay that is $T_{mult}+T_{add}+T_{mux}$ compared with the existing modified Euclid's algorithm and the degree computationless modified Euclid's(DCME) algorithm since it uses new initial conditions. The proposed E-DCME architecture employing a systolic array requires only 2t-1 clock cycles to solve the key equation without initial latency. In addition, the E-DCME architecture consisting of 3t basic cells has regularity and scalability since it uses only one processing element. The E-DCME architecture using the $0.18{\mu}m$ Samsung standard cell library consists of 18,000 gates.