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    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)
    Description.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
    DCField Value Language
    dc.contributor.advisor 李陽明zh_TW
    dc.contributor.author 黃育賢zh_TW
    dc.contributor.author Huang, Yu-Xianen_US
    dc.creator (Authors) 黃育賢zh_TW
    dc.creator (Authors) Huang, Yu-Xianen_US
    dc.date (Date) 2019en_US
    dc.date.accessioned 2019-08-07 16:35:58 (UTC+8)-
    dc.date.available 2019-08-07 16:35:58 (UTC+8)-
    dc.date.issued (Issue Date) 2019-08-07 16:35:58 (UTC+8)-
    dc.identifier (Other Identifiers) G0106751011en_US
    dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124871-
    dc.description (Description) 碩士zh_TW
    dc.description (Description) 國立政治大學zh_TW
    dc.description (Description) 應用數學系zh_TW
    dc.description (Description) 106751011zh_TW
    dc.description.abstract (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。    		zh_TW
    dc.description.abstract (Abstract) 　　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.    		en_US
    dc.description.tableofcontents Abstract　　　i
    摘要　　　ii
    目次　　　iii
    圖目錄　　　iv
    第一章　前言　　　1
    第二章　定義、符號與基本性質　　　3
    第三章　Diffy八邊形　　　9
    第四章　Diffy 2^k邊形　　　15
    第五章　Diffy 2^k邊形彼此間的相關性　　　19
    第六章　Diffy 2^k邊形的分解與其延伸　　　31
    第七章　結論與未來展望　　　43
    參考文獻　　　45    		zh_TW
    dc.format.extent 2552046 bytes-
    dc.format.mimetype application/pdf-
    dc.source.uri (Source URI) http://thesis.lib.nccu.edu.tw/record/#G0106751011en_US
    dc.subject (Keywords) Diffy多邊形zh_TW
    dc.title (Title) Diffy 2^k邊形的探討zh_TW
    dc.title (Title) The study of Diffy 2^k-gonen_US
    dc.type (Data Type) thesisen_US
    dc.relation.reference (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)    		zh_TW
    dc.identifier.doi (DOI) 10.6814/NCCU201900315en_US

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