Diffy 2^k邊形的探討

Abstract

本論文中，我們主要探討Diffy 2^k邊形。在已知Diffy四邊形的一些結果之下，我們首先研究Diffy八邊形，之後，我們將其推廣至一般Diffy 2^k邊形，討論它們的收斂性以及共同性質。\n 接下來，我們研究每一個Diffy 2^k邊形之間，是否存在著某些關聯。本文從「結構」及「數量」兩個大方向去探討彼此間的關係，並得出一些不錯的結果。\n 之後，我們嘗試將Diffy 2^k邊形做分解，將一個邊數多的Diffy多邊形分解成數個邊數較少的Diffy多邊形，以及討論兩種Diffy多邊形它們彼此的關聯。\n 最後，我們嘗試把分解的可行性推廣至更一般的Diffy n邊形，不再只限制於2^k邊形的狀況，也得到了一些結果。而這一部分的研究，也給未來研究一般的Diffy n邊形時，一個很好的起步方向。

In this thesis, we study the Diffy 2^k-gon. Under conditions where some results of Diffy quadrilateral are known, first we study the Diffy octagon, therefore we consider the general Diffy 2^k-gon, and then discuss the convergence and properties between them.\n Second, we study whether there are some relationships between each Diffy 2^k-gon. We discuss the relationships by two directions “construction” and “amount” in this thesis, and we find some good results.\n Third, we try to decompose the Diffy 2^k-gon. We partition a Diffy polygon with more edges into several Diffy polygons with less edges, and discuss the relationships between them.\n Finally, we consider the general Diffy n-gon. We discuss the decomposition of Diffy n-gon, and we also find some results. We think that the result of this part may be a good way to study the general Diffy n-gon in the future.