• Title, Summary, Keyword: analytic geometry

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A Study on Application of Euclid's Geometry at Unit of Equation of Figures in High School 1st Grade (고등학교 도형의 방정식 단원에서 논증기하의 활용에 대한 연구)

  • Kwon, Young-In;Suh, Bo-Euk
    • Communications of Mathematical Education
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    • v.21 no.3
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    • pp.451-466
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    • 2007
  • Geometry in school mathematics is the field that has the possibility of diverse approach such as Synthetic Geometry and Analytic Geometry. Synthetic Geometry is handled in middle schools and Analytic Geometry in the first year of high schools. Therefore, this research show for the possibility of using Synthetic Geometry in high schools which was learned already in middle schools and the way of integrating both of them concretely. This is expected to help students understand the mathematical meaning of figures a lot.

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A Study on the Effectiveness of Dynamic Geometry Software in Solving High School Analytic Geometry Problems. (탐구형 소프트웨어를 활용한 고등학교 해석 기하 교육에 관한 사례 연구)

  • 황우형;차순규
    • The Mathematical Education
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    • v.41 no.3
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    • pp.341-360
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    • 2002
  • The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

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Validity of the Analytic Expression for the Temperature of Joule Heated Nano-wire

  • Ha, Seung-Seok;You, Chun-Yeol
    • Journal of Magnetics
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    • v.12 no.1
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    • pp.7-11
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    • 2007
  • We confirm the validity of the analytic expression for the temperature of the Joule heated nano-wire [C.-Y. You et al. Appl. Phys. Lett. 89, 222513 (2006)] with finite element method. The temperature of the Joule heated nano-wire is essential information for the research of the current induced domain wall movement. The analytic expression includes an adjustable parameter which must be determined. Since the physical origin of the adjustable parameter is simplification of the heat source profile, the validity of the analytic expression must be examined for wide range of the nano-wire structure. By comparison with this analytic expression with the results of full numerical finite element method, the adjustable parameter has been determined. The numerically confirmed adjustable parameter values are in the range of 0.60$\sim$0.69, which is well matched with the theoretically expected one. Furthermore, it is found that the adjustable parameter is a slow varying function of the nano-wire geometry. Based on this numerical confirmation, we can apply the analytic expression for the wide range of the nano-wire geometry with proper adjustable parameters.

Designing and Implementing High School Geometry Lessons Emphasizing the Connections between Euclidean and Analytic Geometries (GeoGebra를 활용한 논증기하와 연결된 해석기하 수업자료 개발 및 적용)

  • Kim, Eun Hye;Lee, Soo Jin
    • Journal of the Korean School Mathematics Society
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    • v.19 no.4
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    • pp.373-394
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    • 2016
  • The "Figure Equation" chapter of current high school curriculum prevents students from relating the concept with what they studied in middle school Euclidean geometry. Woo(1998) concerns that the curriculum introduces the concept merely in algebraic ways without providing students with opportunities to relate it with their prior understanding of geometry, which is based on Euclidean one. In the present study, a sequence of GeoGebra-embedded-geometry lessons was designed so that students could be introduced to and solve problems of the Analytic Geometry by triggering their prior understanding of the Euclidean Geometry which they had learnt in middle school. The study contributes to the field of mathematics education by suggesting a sequence of geometry lessons where students could introduce to the coordinate geometry meaningfully and conceptually in high school.

The Approximate Realization of Ab$\={u}$ Sahl's Geometric Construction about a Heptagon through GSP using Conic Sections (이차곡선을 활용한 정칠각형에 관한 Ab$\={u}$ Sahl의 작도법의 GSP를 통한 재조명)

  • Kim, Hyang-Sook;Pak, Jin-Suk;Ha, Hyoung-Soo
    • The Mathematical Education
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    • v.50 no.2
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    • pp.233-246
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    • 2011
  • The geometry field in the current high school curriculum deals mainly with analytic geometry and the reference to logic geometry leaves much to be desired. This study investigated the construction on a heptagon by using conic sections as one of measures for achieving harmony between analytic geometry and logic geometry in the high school curriculum with the Geometer's Sketchpad(GSP), which is a specialized software prevalent in mathematics education field and is intended to draw an educational suggestion on it.

Conflict of Synthesis and Analysis: from heuristic until method of projective Geometry (종합과 해석의 대립 : 발견술에서 사영기하학의 방법론까지)

  • Han, Kyeong-Hye
    • Journal for History of Mathematics
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    • v.18 no.4
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    • pp.29-38
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    • 2005
  • This Paper discusses the history of the conflicts between synthesis and analysis, from those in heuristic and logic development style in ancient Greek to those in projective geometric methods. The two methods, which originally displayed difference in heuristic, offer the base for the two fields of geometry, the analytic geometry and the synthetic geometry in the 18th century as they originated from the field of geometry. As to the 19th century, they even display antagonistic aspects derived by having other perspectives about the true nature of mathematic but finally lose the reason of conflict as the ancient times when the dialectical sublation of both had been proposed.

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A study on the analytic geometric characteristics of Archimedes' 《The Method》 and its educational implications (아르키메데스의 《The Method》의 해석기하학적 특성과 그 교육적 시사점에 대한 연구)

  • Park, Sun-Yong
    • Journal for History of Mathematics
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    • v.27 no.4
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    • pp.271-283
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    • 2014
  • This study takes a look at Polya's analysis on Archimedes' "The Method" from a math-historical perspective. We, based on the elaboration of Polya's analysis, investigate the analytic geometric characteristics of Archimedes' "The Method" and discuss the way of using the characteristics in education of school calculus. So this study brings up the educational need of approach of teaching the definite integral by clearly disclosing the transition from length, area, volume etc into the length as an area function under a curve. And this study suggests the approach of teaching both merit and deficiency of the indivisibles method, and the educational necessity of making students realizing that the strength of analytic geometry lies in overcoming deficiency of the indivisibles method by dealing with the relation of variation and rate of change by means of algebraic expression and graph.

Re-Interpreting the Descartes's Perspectives on the Connection of Algebra and Geometry (대수와 기하의 연결에 관한 Descartes의 관점 재조명 연구)

  • Ban, Eun Seob;Shin, Jaehong;Lew, Hee Chan
    • Journal of Educational Research in Mathematics
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    • v.26 no.4
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    • pp.715-730
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    • 2016
  • The purpose of this study is to analyze Descartes's point of view on the mathematical connection of algebra and geometry which help comprehend the traditional frame with a new perspective in order to access to unsolved problems and provide useful pedagogical implications in school mathematics. To achieve the goal, researchers have historically reviewed the fundamental principle and development method's feature of analytic geometry, which stands on the basis of mathematical connection between algebra and geometry. In addition we have considered the significance of geometric solving of equations in terms of analytic geometry by analyzing related preceding researches and modern trends of mathematics education curriculum. These efforts could allow us to have discussed on some opportunities to get insight about mathematical connection of algebra and geometry via geometric approaches for solving equations using the intersection of curves represented on coordinates plane. Furthermore, we could finally provide the method and its pedagogical implications for interpreting geometric approaches to cubic equations utilizing intersection of conic sections in the process of inquiring, solving and reflecting stages.

The reinterpretation and visualization about trisecting general angle in Medieval Islam using conic sections (원뿔곡선을 이용한 중세 이슬람의 일반각의 3등분문제의 재조명과 시각화)

  • Kim, Hyang Sook;Kim, Mi Yeoun;Park, Jae Hyun
    • East Asian mathematical journal
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    • v.35 no.2
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    • pp.141-161
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    • 2019
  • The purpose of this paper is to reinterpret and visualize the trisection line construction of general angle in the Medieval Islam using conic sections. The geometry field in the current 2015 revised Mathematics curriculum deals mainly with the more contents of analytic geometry than logic geometry. This study investigated four trisecting problems shown by al-Haytham, Abu'l Jud, Al-Sijzī and Abū Sahl al-Kūhī in Medieval Islam as one of methods to achieve the harmony of analytic and logic geometry. In particular, we studied the above results by 3 steps(analysis, construction and proof) in order to reinterpret and visualize.

Skemp's concept development of underachievers' analytic geometry using the exploratory software, GSP & Excel (탐구형 소프트웨어를 활용한 해석기하에서 학습부진학생들의 개념형성에 관한 연구: 관계적.도구적 이해를 중심으로)

  • Yoon, In Jun;ChoiKoh, Sang Sook
    • Journal of the Korean School Mathematics Society
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    • v.15 no.4
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    • pp.643-671
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    • 2012
  • The purpose of this study was to examine How the exploratory activities using Excel and GSP which are exploratory software, in learning analytic geometry affected on the underachievers' analytic geometry concept development process. The subjects of 5 students who received the 8th~9th grades from their examination of the last semester, participated in a total of 7 units based on Skemp's intelligent learning model. The results of the study showed that there were two important cases found to nearly achieve the category $R_2$. One was reflective thinking could happen through exploratory software in category $R_1$. The other was the exploratory activities which could have the same effectiveness as the relational understanding in category $I_2$, as Skemp mentioned that there is a room to be achieved in the elementary level when such relational understanding is achieved.

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