• Communications of Mathematical Education
• /
• v.24 no.3
• /
• pp.659-689
• /
• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• Journal of the Korean School Mathematics Society
• /
• v.24 no.1
• /
• pp.39-57
• /
• 2021

In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.

• Journal for History of Mathematics
• /
• v.19 no.2
• /
• pp.101-114
• /
• 2006

The content and method of geometry taught in secondary school is rooted in 'Elements' by Euclid. On the other hand, however, there are differences between the content and structure of the current textbook and the 'Elements'. The gaps are resulted from attempts to develop the geometry education. Specially, the content and method for the proportional relations of geometric figures has been varied. In this study, we reviewed the changes of the proportional relations of geometric figures with pedagogical point of view. The conclusion that we came to is that the proportional relations in incommensurable case Is omitted in secondary school. Teacher's understanding about the proportional relations of geometric figures is needed for meaningful geometry education.

• Communications of Mathematical Education
• /
• v.25 no.3
• /
• pp.577-591
• /
• 2011

In this study, in order to use computer in mathematical learning effectively, we investigate application of computer shown textbooks in geometry unit of middle school mathematics. First, we analyzed about status of computer application and method of computer application in 27 textbooks. We presented concrete example of mathematics activity using computer that can be used by teachers. Also, we tried to find out the direction to use computer more effectively in teaching and learning geometry. Through this process, we do not simply use computer to play for interest but to use it more meaningfully.

• Journal of the Korean School Mathematics Society
• /
• v.2 no.1
• /
• pp.121-131
• /
• 1999

Recently our educational methodologies have been changed to an open, student-centered structure. Mathematics is now learned through experiential interaction and less emphasis is placed on abstract theories. For example, the axioms of the geometry in the middle school curriculum have been expressed by using symbolic letters. Students find these abstractions very difficult and it hinders their ability to grasp the significance of geometrical concepts. In an effort to simplify these abstract concepts and enhance the students interest and ability to learn, the GSP (Geometry Sketchpad) is proving to be a useful and effective tool. First, Second and third grade students have found the GSP to be extremely useful. While the pad has no sound function it still enables the students to freely change diagrams without disrupting the integrity of the program. There is also a running order of instructions at the bottom of the screen to facilitate the step by step understanding of mathematical procedures. This function makes the program ideal for use by teachers, students and even beginners. Anyone experiencing difficulty can get immediate assistance from the guidebook which is located at the back of each program. Allowing individuals to manipulate and actually see the changing deductions and axiom proofs on the computer screen provides them with immediate feedback and reinforcement. It also enhances their overall interest in learning geometry. The use of the GSP is proving to be an innovative and effective tool in facilitating the transition of mathematics into an open, student-centered educational forum.

• School Mathematics
• /
• v.9 no.4
• /
• pp.523-533
• /
• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• The Journal of Advanced Prosthodontics
• /
• v.6 no.6
• /
• pp.547-554
• /
• 2014

Implant success is achieved by the synergistic combination of numerous biomechanical factors. This report examines the mechanical aspect of implants. In particular, it is focused on macrodesign such as thread shape, pitch, width and depth, and crestal module of implants. This study reviews the literature regarding the effect of implant thread geometry on primary stability and osseointegration under immediate loading. The search strategy included both in vitro and in vivo studies published in the MEDLINE database from January 2000 to June 2014. Various geometrical parameters are analyzed to evaluate their significance for optimal stress distribution, implant surface area, and bone remodeling responses during the process of osseointegration.

• School Mathematics
• /
• v.4 no.1
• /
• pp.15-27
• /
• 2002

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them. Definitions use din academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about let·els of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics.

• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.419-428
• /
• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• Journal for History of Mathematics
• /
• v.20 no.2
• /
• pp.73-88
• /
• 2007

In this paper, we study the symmetry of figures in elementary geometry. First, we investigate the historical and mathematical background of symmetry of figures and we explore the suitable teaching and learning methods for symmetry in elementary geometry. Also we study the major problem of geometry education that occurring in elementary school.