볼록 사각형의 Macbeath inconic과 볼록 사각형의 Orthic inconic에 대한 연구

Abstract

This study was based on the research results conducted as an R&E project for gifted students with financial support from the Korea Foundation for the Advancement of Science and Creativity. In this study, the Macbeath inconic and Orthic inconic defined in triangles are expanded to convex quadrilateral to study the Macbeath inconic of convex quadrilaterals and the Orthic inconic of convex quadrilaterals. Through this study, the following research results are obtained. First, it is discovered that the condition for a quadrilateral in which the Macbeath inconic of a convex quadrilateral exists. Second, the locations of the two foci of the Macbeath inconic of convex quadrilateral were found. Third, this study also reveals the formulas for the length of the major axis, the length of the minor axis, and the area of the Macbeath inconic of convex quadrilaterals. Fourth, the study unveils the division ratio of the Macbeath inconic of convex quadrilateral. Fifth, it is also discovered that the condition for a quadrilateral in which an orthic inconic of a convex quadrilateral exists. Sixth, the uniqueness of the orthic inconic of the convex quadrilateral is proven. Seventh, the area formula for the orthic inconic of a convex quadrilateral is derived. Lastly, this study shows the division ratio of the orthic inconic of the convex quadrilateral. It is expected that expanding and studying mathematical concepts into a wider area, as in this study, will contribute to the development of mathematics.