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평면상의 점집합에서의 볼록 다각형에 관한 고찰

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Author(s)
안성윤
Issued Date
2009
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.
Alternative Title
A study on the convex polygons in planar point sets
Alternative Author(s)
An Sung-yoon
Affiliation
조선대학교 교육대학원
Department
교육대학원 수학교육
Advisor
강은실
Awarded Date
2009. 8
Table Of Contents
- 목 차-

ABSTRACT


Ⅰ. 서 론 1

A. 이론적 배경 1

Ⅱ. 본 론 3

A. 볼록 다각형 3
1. 볼록 삼각형과 사각형 3
2. 볼록 오각형 8
B. 속이 빈 볼록 다각형 13
1. 속이 빈 볼록 삼각형과 사각형 14
2. 속이 빈 볼록 오각형 15

Ⅲ. 결 론 25
참고문헌 26
Degree
Master
Publisher
조선대학교 대학원
Citation
안성윤. (2009). 평면상의 점집합에서의 볼록 다각형에 관한 고찰
Type
Dissertation
URI
https://oak.chosun.ac.kr/handle/2020.oak/5061
http://chosun.dcollection.net/common/orgView/200000238500
Appears in Collections:
Education > Theses(Master)(교육대학원)
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