평면상의 점집합에서의 볼록 다각형에 관한 고찰

Abstract

ABSTRACT A study on the convex polygons in planar point sets

An Sung-yoon Advisor : Prof. Kang Eun-sil Ph.D. Major in Mathematics Education Graduate School of Education, Chosun University

In 1935, Erd？s and Szekeres posed the problem of determining the smallest positive integer so that any set of at least points in general position in the plane contains a convex -gon. Until now, the problem has been solved for the values , and 5 only. In this thesis, we will show that and . Also, Erd？s posed a similar problem on empty convex polygons, which is of determining a smallest positive integer such that any set of at least points in general position in the plane contains an empty convex -gon. For and 4, it is easy to show that . For , Harborth proved that . In this thesis, we reprove that by visualizing the method of Harborth.