• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.11
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• pp.39-46
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• 1997

In this paper, we propose an area-efficient architecture of a reed-solomon (RS) decoder/encoder for digital VCRs. The new architecture of the decoder/encoder targeted to reduce the circit size and decoding latency has the following two features. First, area-efficeincy has been significantly improved by sharing a functional block for encoding, modified syndrome computation, and erasure locator polynomial evaluation. Second, modified euclid's algorithms has been implemented by using a new architecture. Experimental results have showed that the decoder/encoder designed by using the proposed method has been implemented with 25% smaller sie over straight forware implementation based on the conventional method [1] and the decoding latency has been reduced.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.251-263
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• 2004

피타고라스 정리와 코사인 제 2법칙 사이에는 어떤 관계가 있을까. 현재 우리의 교육과정에서는 피타고라스 정리는 중학교 3학년에서 코사인 제 2법칙은 고등학교 1학년에서 배운다. 그런데, 이 두 가지 수학적 사실 사이에는 밀접한 관계가 있다. 피타고라스 정리의 확장으로서 코사인 제 2법칙을 유도할 수 있다는 것이다. 코사인 제2법칙이 소개되어진 최초의 문헌은 Euclid의 <원론>으로 거슬러 올라간다. <원론>에 소개되어진 코사인 제 2법칙의 증명방법으로 시작하여 수 천년 동안 증명되어온 다양한 증명방법을 소개하고자 한다. 특히, 직각삼각형과 원이라는 큰 틀을 바탕으로 코사인 제 2법칙의 증명 방법에 대해 고찰하고, 그 외 다양한 증명방법을 분석하고자 한다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.521-527
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• 1997

Irregular shapes and growth behavior of surface micro-crack showed very complex and nonlinear propeties and many investigators have performed theoretical analysesand experiments on them to characterize fatigue strength. They had difficulties in estimating fatigue life due to random distribution, growth and coalescence of surface micro-cracks. The straightness of crack growth along intergranular and transgranular was prevented from irregular microstructure and precipitates. Euclid geometry can't quantify shape of surface micro-crack but ftractal geometry can. Therefore, it is suggested that average fractal dimension of surface micro-cracks is able to estimate fatigue life but fractal dimension of maximum surface micro-crack is not in Al 2024-T3 alloy.

• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.549-552
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• 2003

In this paper, an efficient architecture of a versatile Reed-Solomon (RS) decoder is designed, where the message length k as well as the block length n can be variable. The decoder permits 3-step pipelined processing based on the modified Euclid's algorithm(MEA). A new architecture for the MEA is designed for variable values of error correcting capability t. To maintain the throughput rate with less circuitry, the MEA block uses both the recursive and the overclocking technique. The decoder can decode a codeword received not only in a burst mode, but also in a continuous mode. It can be used in a wide range of applications due to its versatility. A versatile RS decoder over GF(2$^{8}$ ) having the error-correcting capability of up to 10 has been designed in VHDL, and successfully synthesized in an FPGA chip.

• Journal for History of Mathematics
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• v.33 no.4
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• pp.223-236
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• 2020

We examine how the formulas of the area and the circumference of a circle related to pi in the ancient Egyptian and the Old Babylonian fields of mathematics have been controversial. In particular, the Great Pyramid of Khufu, Ahmes Papyrus Problem 48 and Moscow Mathematical Papyrus Problem 10 have raised extensive controversy over π. We propose the pi-theory of the Great Pyramid of Khufu as a dynamic symmetry based on Euclid's rectangle. In addition, we argue that the ancient Egyptian or Old Babylonian mathematics influenced Solomon's Molten Sea, Plato and Archimedes' pi.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.3A
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• pp.231-237
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• 2010

Multi-input multi-output (MIMO) systems are used to improve the transmission rate in proportion to the number of antennas. However, their computational complexity is very high for the detection in the receiver. The sphere decoding (SD) is a detection algorithm with reduced complexity. In this paper, an improved Schnorr-Euchner SD (SE SD) is proposed based on the minimum mean square error (MMSE) and the Euclidean distance criteria without additional complexity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.245-246
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• 2006

For developing 5-axis laser cutting systems, many problems such as rotating of laser head or table, 5-axis tool path generation and collision avoidance between laser head and product should be solved. In this paper, a five-axis laser cutting machine with table swivel and rotary type configuration is developed. The five axes (X,Y,Z,A,B) are controlled and interfaced to PC via MMC board. Two kinds of CAM S/W such as commercial 5-axis CAM S/W(Euclid) and UG-API are engaged to generate NC code for the developed 5-axis laser cutting machine.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.738-741
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• 1988

In this paper, we deal with the movements identification of EMG signals by LPC cepstrum coefficients. Movements were identified by extration of characteristics of similar patterns in Euclid distance measurement method for EMG signals generated by voluntary contractions of subject's musculature. As number of coefficients is larger, we obtain the better rate of movements identification. By exact extraction of signals and decision of optimal coefficient, it is expected that these results will apply to prosthesis control in real-time.