Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/124871`

 Title: Diffy 2^k邊形的探討The study of Diffy 2^k-gon Authors: 黃育賢Huang, Yu-Xian Contributors: 李陽明黃育賢Huang, Yu-Xian Keywords: Diffy多邊形 Date: 2019 Issue Date: 2019-08-07 16:35:58 (UTC+8) 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。　　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。　　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。　　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.　　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.　　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.　　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. Reference: [1] M. Burmester, R. Forcade and E. Jacobs, Circles of Numbers. Glasgow Mathematical Journal, 19:115-119. (July 1978)[2] P. T. Bateman, Cycles of Differences of Integers. Journal of Number Theory, volume 13, 255-261. (May 1981)[3] 王偉名, Diffy六邊形之探討(A Study about Diffy Hexagon). National Chengchi University, (2014)[4] 林亨峰, 迪菲七邊形(Diffy Heptagon). National Chengchi University, (2013)[5] 黃信弼, Diffy Pentagon. National Chengchi University, (2012)[6] 蔡秀芬, 迪菲方塊(Diffy Box). National Chengchi University, (2008) Description: 碩士國立政治大學應用數學系106751011 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0106751011 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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