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https://nccur.lib.nccu.edu.tw/handle/140.119/124871
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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) |
| 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 |
| DOI: | 10.6814/NCCU201900315 |
| Appears in Collections: | [應用數學系] 學位論文
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| 101101.pdf | 2492Kb | Adobe PDF2 | 113 | View/Open |
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