• Title/Summary/Keyword: Pythagorean theorem

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구고호은문에 대한 고찰

  • 호문룡
    • Journal for History of Mathematics
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    • v.15 no.1
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    • pp.43-56
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    • 2002
  • Hong, Jung-Ha(1684-\ulcorner ) explained 78 problems which look for the length of right triangle satisfying the given conditions by the Pythagorean theorem or the ratio of similarity in the chapter ‘Goo-Go-Hoh-Eun-Moon’of the 5th volume of his book Goo-Ill-Jeep. Most questions are formulated by equations of degree 2, 3, 4 which mostly have rational number solutions and part of the equations are expressed by counting stick. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with a few steps to solve.

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FIXED POINT THEOREMS IN b-MENGER INNER PRODUCT SPACES

  • Rachid Oubrahim
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.2
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    • pp.487-499
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    • 2024
  • The main motivation for this paper is to investigate the fixed point property for nonlinear contraction defined on b-Menger inner product spaces. First, we introduce a b-Menger inner product spaces, then the topological structure is discussed and the probabilistic Pythagorean theorem is given and established. Also we prove the existence and uniqueness of fixed point in these spaces. This result generalizes and improves many previously known results.

Development of a Model for the Process of Analogical Reasoning (유추 사고과정 모델의 개발)

  • Choi, Nam Kwang;Lew, Hee Chan
    • Journal of Educational Research in Mathematics
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    • v.24 no.2
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    • pp.103-124
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    • 2014
  • The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

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Analysis of the Waistline and the Back Waist Point of Slacks Pattern for Optimizing the Range of Motion (동작적합성을 위한 슬랙스 패턴의 허리선 및 허리뒤점 설계에 관한 연구)

  • Kwon, Sook-Hee;Hong, Ji-Un
    • Journal of the Korean Home Economics Association
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    • v.47 no.4
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    • pp.61-72
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    • 2009
  • The purpose of this research is to suggest a new way to approach measuring the waist line of slacks. The pattern formulated enables a construction method that optimizes motion. The method is based on the measurement on the length change of the body surface line. The research reveals: 1. The analysis of expansion and contraction by area showed that G8 markedly shrunk, whilst G15 maximally stretched during M4 motion. 2. The areas that stretched during M2 motion were, in order of size: G10, G17, G16, and G8. Conversely, the areas that shrunk are, in order, G9, G11, and G18. The areas that stretched during M3 motion were G10, G17, G16, G12, and G15; the areas that shrunk were G9, G11, G18, and G8. 3. In constructing the slacks pattern to allow for appropriate movement, we calculated the length between the knee and back of the waist, point (y), using Pythagoras’theorem and trigonometry. The equation was y = 1.005x. 4. In the two pattern N method and L method, y is equal or less than x, but for our research pattern, y was larger than x

A critical review on middle school mathematics curriculum revised in 2011 focused on geometry (2011 중학교 수학과 교육과정의 비판적 고찰: 기하 영역을 중심으로)

  • Park, Kyo-Sik;Kwon, Seok-Il
    • Journal of Educational Research in Mathematics
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    • v.22 no.2
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    • pp.261-275
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    • 2012
  • There are some geometry achievement standards presented indistinctly in middle school mathematics curriculum revised in 2011. In this study, indistinctness of some geometric topics presented indistinctly such as symbol $\overline{AB}{\perp}\overline{CD}$ simple construction, properties of congruent plane figures, solid of revolution, determination condition of the triangle, justification, center of similarity, position of similarity, middle point connection theorem in triangle, Pythagorean theorem, properties of inscribed angle are discussed. The following three agenda is suggested as conclusions for the development of next middle school mathematics curriculum. First is a resolving unclarity of curriculum. Second is an issuing an authoritative commentary for mathematics curriculum. Third is a developing curriculum based on the accumulation of sufficient researches.

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조선조대 호실전적의 허실과 삼각함수표

  • 유인영
    • Journal for History of Mathematics
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    • v.15 no.3
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    • pp.1-16
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    • 2002
  • The area between the arc and chord of a circle is called Hosichun whose figure looks like a bow and an arrow, and had been evaluated by the two formulas $\textit{H}_{n1}$=a(a+y)/2 and $\textit{H}_{n2}$=3ay/4, where $\alpha$ is the length of the arrow and y the chord of the circle. By the inspection of the area of the Hosichun, some errors of the numeration table in Thurmans S. Peterson's CALCULUS were found easily, that is, the area of the Hosichun is smaller than its subarea in the same Hosichun and perhaps has been to be the worldwide and centurial invalid standard. From now on, the chain proofreadings of the errors will be necessary in our mathematical world. This paper is intended to introduce some such problems related to a circle and another Pythagorean Theorem which is the ratio of the side and diagonal of five and seven In a square.

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Designing Mathematical Activities Centered on Conjecture and Problem Posing in School Mathematics (학교수학에서 추측과 문제제기 중심의 수학적 탐구 활동 설계하기)

  • Do, Jong-Hoon
    • The Mathematical Education
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    • v.46 no.1 s.116
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    • pp.69-79
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    • 2007
  • Students experience many problem solving activities in school mathematics. These activities have focused on finding the solution whose existence was known, and then again conjecture about existence of solution or posing of problems has been neglected. It needs to put more emphasis on conjecture and problem posing activities in school mathematics. To do this, a model and examples of designing mathematical activities centered on conjecture and problem posing are needed. In this article, we introduce some examples of designing such activities (from the pythagorean theorem, the determination condition of triangle, and existing solved-problems in textbook) and examine suggestions for mathematics education. Our examples can be used as instructional materials for mathematically able students at middle school.

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Teaching of the Meaning of Proof Using Historic-genetic Approach - based on Pythagorean Theorem - (역사.발생적 전개를 따른 증명의 의미 지도 - 피타고라스 정리를 중심으로 -)

  • Song, Yeong-Moo;Lee, Bo-Bae
    • School Mathematics
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    • v.10 no.4
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    • pp.625-648
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    • 2008
  • We collected the data through the following process. 36 third-grade middle school students are selected, and we conducted ex-ante interviews for researching how they understand the nature of proof. Based on the results of survey, then we chose two students we took a lesson with the Branford's among the 36 samples. After sampling, historic-genetic geometry education, inspected carefully whether the Branford's method helps the students.

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Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 수학적(數學的) 구조(構造))

  • HONG, Sung Sa;HONG, Young Hee;LEE, Seung On
    • Journal for History of Mathematics
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    • v.28 no.6
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    • pp.301-310
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    • 2015
  • Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.