학술논문
작도에 관한 고찰
Document Type
Dissertation/ Thesis
Author
Source
Subject
Language
Korean
Abstract
본 연구는 작도에 관한 다양한 성질들을 고찰하여 학교수학에 대한 교수학적 자료를 제공하고자 하였다. 본 고찰에서 다룬 내용을 구체적으로 요약하면 다음과 같다. 첫 번째, 작도에 관한 다양한 선행 연구 및 문헌을 분석하였다. 두 번째, 7차 개정 교육과정의 중학교 교과서에 나오는 작도 문제를 작도의 4단계에 맞추어 정리하였다. 세 번째, 3대 작도 문제의 유래와 그 해결과정을 알아보고, 해결과정에서 나온 작도 가능한 수를 분류하여 정리하였다. 네 번째, 히포크라테스의 궁형구적법을 알아보고, 정3, 4, 5, 15, 17각형의 작도법과 작도 가능한 정다각형과 작도 불가능한 정다각형을 분류하였다. 마지막으로 컴퍼스와 눈금 없는 자로만 작도 가능한 문제를 컴퍼스로만 작도 가능하다고 하였던 마스케로니의 정리를 알아보았다. 이 연구를 통하여 많은 사람들이 기하학 공부에 흥미를 느끼고 수학에 관심을 가질 수 있기를 기대한다.
This study examined diverse characteristics of constructing to provide pedagogical data for school math. Details investigated in this paper are summarized as below. Firstly, this paper analyzes various advanced researches and literatures on constructing figures. Secondly, this study arranges questions to constructed figures contained in the middle school textbooks of the 7th National Curriculum revised according to the 4 steps of constructing figures. Thirdly, this research examines the origin of the three greatest questions to constructed figures and the process of their solutions and also arranges the possible number of constructing figures gained through the process of solving. Fourthly, this article examines Hippocrates’ mensuration and methods to constructed regular 3-angled, 4-angled, 5-angled, 15-angled, and 17-angled shapes and also classifies regular polygons that can be constructed or cannot be constructed. Lastly, this paper studies Mohr-Mascheroni theorem which says figures that can be constructed with a compass and a gradation-less ruler also can be constructed only with a compass. It is expected that this research will attract a lot of people to have interest in studying geometry and also math.
This study examined diverse characteristics of constructing to provide pedagogical data for school math. Details investigated in this paper are summarized as below. Firstly, this paper analyzes various advanced researches and literatures on constructing figures. Secondly, this study arranges questions to constructed figures contained in the middle school textbooks of the 7th National Curriculum revised according to the 4 steps of constructing figures. Thirdly, this research examines the origin of the three greatest questions to constructed figures and the process of their solutions and also arranges the possible number of constructing figures gained through the process of solving. Fourthly, this article examines Hippocrates’ mensuration and methods to constructed regular 3-angled, 4-angled, 5-angled, 15-angled, and 17-angled shapes and also classifies regular polygons that can be constructed or cannot be constructed. Lastly, this paper studies Mohr-Mascheroni theorem which says figures that can be constructed with a compass and a gradation-less ruler also can be constructed only with a compass. It is expected that this research will attract a lot of people to have interest in studying geometry and also math.