• Title/Summary/Keyword: 필산

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A Study of the Representation and Algorithms of Western Mathematics Reflected on the Algebra Domains of Chosun-Sanhak in the 18th Century (18세기 조선산학서의 대수 영역에 나타난 서양수학 표현 및 계산법 연구)

  • Choi, Eunah
    • Journal of the Korean School Mathematics Society
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    • v.23 no.1
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    • pp.25-44
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    • 2020
  • This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

Gate Sizing Of Multiple-paths Circuit (다중 논리경로 회로의 게이트 크기 결정 방법)

  • Lee, Seungho;Chang, Jongkwon
    • KIPS Transactions on Computer and Communication Systems
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    • v.2 no.3
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    • pp.103-110
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    • 2013
  • Logical Effort [1, 2] is a simple hand-calculated method that measures quick delay estimation. It has the advantage of reducing the design cycle time. However, it has shortcomings in designing a path for minimum area or power under a fixed-delay constraint. The method of overcoming the shortcomings is shown in [3], but it is constrained for a single logical path. This paper presents an advanced gate sizing method in multiple logical paths based on the equal delay model. According to the results of the simulation, the power dissipation for both the existing logical effort method and proposed method is almost equal. However, compared with the existing logical effort method, it is about 52 (%) more efficient in space.

On a Logical Path Design for Optimizing Power-delay under a Fixed-delay Constraint (고정 지연 조건에서 전력-지연 효율성의 최적화를 위한 논리 경로 설계)

  • Lee, Seung-Ho;Chang, Jong-Kwon
    • The KIPS Transactions:PartA
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    • v.17A no.1
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    • pp.27-32
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    • 2010
  • Logical Effort is a simple hand-calculated method that measures quick delay estimation. It has the advantage of reducing the design cycle time. However, it has shortcomings in designing a path for minimum area or power under a fixed-delay constraint. In this paper, we propose an equal delay model and, based on this, a method of optimizing power-delay efficiency in a logical path. We simulate three designs of an eight-input AND gate using our technique. Our results show about 40% greater efficiency in power dissipation than those of Logical Effort method.

Mathematics Textbook in Korea (1880-2016) (한국 근·현대수학 교재 연구)

  • Lee, Sang-Gu;Lee, Jae Hwa;Kim, Yeung-Gu;Lee, Kang Sup;Ham, Yoonmee
    • Communications of Mathematical Education
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    • v.31 no.1
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    • pp.149-177
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    • 2017
  • Since modern mathematics textbooks were introduced in the late 19th century Korea, arithmetic experts started to teach modern mathematics using Arabic numerals at village schools and churches. After the Gabo Education Reform of 1894, western mathematics education was included in public education and the mathematics textbooks began to be officially published. We explored most of Korean mathematics textbooks from 1895 to 2016 including the changes of mathematics curriculum through 1885-1905, 1905-1910, 1911-1945, 1945-1948, 1948-1953, 1954-1999, and 2000-2016. This study presents the characters of modern mathematics textbooks of Korea since 1885.

Design Charts and Simplified Formulae for Anchored Sheet Pile Wall- Using Equivalent Beam Analysis for Fixed End Supported Wall - (앵커식 널말뚝벽의 설계용 도표와 간편식- 고정지지 널말뚝의 등가보 해석을 사용하여 -)

  • 김기웅;원진오;백영식
    • Journal of the Korean Geotechnical Society
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    • v.16 no.1
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    • pp.19-30
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    • 2000
  • The major design parameters of the anchored sheet-pile wall include the determination of required penetration depth, the force acting on the anchor, and the maximum bending moment in the piling. Blum solved the fixed earth supported wall using the equivalent beam method, assuming that the wall can be separated into upper and lower parts of the point of contraflexure. Design charts help designer by simplifying the design procedure. But they have some difficulties under some Geotechnical and geometrical conditions. For example, the conventional design charts can compute design parameters only when the ground water table exists above the dredge line. In this paper, the design charts which can be used for the ground water table existing under the dredge line are presented. And simplified formulae are developed by regression analysis. It is found that simplified formulae are not only very useful for the practice of design but also they can evaluate the result of numerical methods or design charts.

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A study on the transition of the representations of numbers and mathematical symbols in Joseon mathematics (조선산학의 수학적 표현의 변천에 대한 고찰 - 수와 연산, 문자와 식 영역을 중심으로 -)

  • Choi, Eunah
    • Communications of Mathematical Education
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    • v.28 no.3
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    • pp.375-394
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    • 2014
  • The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

A review on teaching contents in area of Korean math textbook for first grade - even and odd number, composition and decomposition of numbers, calculation with carrying or with borrowing - (우리나라 초등학교 1학년 수학 교과서 <수와 연산> 영역의 지도 내용 검토 - 짝수.홀수, 수의 합성.분해, 받아올림.받아내림이 있는 계산 -)

  • Lee, Seung;Choi, Kyoung A;Park, Kyo Sik
    • Journal of the Korean School Mathematics Society
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    • v.18 no.1
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    • pp.1-14
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    • 2015
  • In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.