Discussing the Happy Ending problem from the Paul Erdős-Szekeres Theory

• Main Authors: Fu-Cyuan Wun, 溫福銓
• Other Authors: Chin-Tung Wu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/55678263536694566103

碩士 === 國立屏東教育大學 === 應用數學系 === 99 === In 1935, Esther Klein [1] asked, “Is it true that for every n, there is a least value g(n) such that any set of g(n) points in the plane in general position always contains the vertices of a convex n-gon?” This is the “Happy Ending problem” because it led to the marriage of George Szekeres and Esther Klein. In this paper, we show the existence of g(n) and estimate its upper bound and lower bound by using the Erdős-Szekeres Theorem. We also constructing explicit examples for the minimal possible g(n) for a set of g(n) points in the plane in general position must contain a convex n-gon.