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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:[Department of Mathematical Sciences] Theses

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