원문정보
A Study on the Meaning of Construction in Euclid Elements
초록
영어
The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.
한국어
고대 그리스 시대의 작도는 현 교육에서의 작도 이상의 의미를 지닌 것이었다. 본 연구는 이러한 사실에 입각하여 현 교과서의 작도 의미를 살펴보고, 이와 대비되는
목차
Ⅰ. 서론
Ⅱ. 교과서의 작도 의미
Ⅲ.
1. 공준으로 타당성을 확보한 추상적 활동
2. 도형의 존재성 입증 및 논증에서 보조선 도입의 타당성 확보 수단
3. 보조선 도입 이외의 논증 개입 자제
4. 수와 대수를 다루는 수단
Ⅳ. 작도의 교육적 활용
1. 논증에 보조선 도입의 타당성 확보 수단으로서의 작도 활용의 이점
2. Euclid 도구로 작도 불가능한 보조선에 대한 관점 논의
Ⅴ. 맺는 글
참고문헌
Abstract