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題名 迪菲方塊
Diffy Pentagon
作者 黃信弼
貢獻者 李陽明
黃信弼
關鍵詞 迪菲五邊形
強勢數學歸納法
Diffy pentagon
Strong induction
日期 2012
上傳時間 1-Nov-2012 13:58:08 (UTC+8)
摘要 在迪菲方塊中，我們將正方形的四個頂點皆填入數值，再利用相鄰兩頂點相減，再取絕對值的方式觀察其數列行為，發現四個頂點的數字最後皆會收斂至0。在本文中，我們將之推廣至五邊形，我們稱它為迪菲五邊形。我們套用同樣的運算模式後，發現亦有特殊的收斂行為。
In Diffy box, we write down numbers on the four vertices of square, and then on the midpoint of each side write the difference between the two numbers at its endpoints. It is known that the numbers on the four vertices of a square will converge to zero finally. In this article, we use the same operations as Diffy box to discuss pentagons which we call" Diffy pentagon ". We find it will converge, too.
參考文獻 [1] A. Behn, C. Kribs-Zaleta, and V. Ponomarenko, The Convergence of Difference Boxes. American Math. Monthly, volume 112, 426-438, (1995)
[2] F. Breuer, Ducci Sequences in Higher Dimensions. Electronic Journal of Combinatorial
Number Theory 7, #A24, (2007)
[3] R. Brown and J. Merzel, The Length of Ducci’s Four-Number Game. Rocky Mountain
Journal of Mathematics, volume37, 45-65, (2007)
[4] N. Calkin, J. Stevens, and D. Thomas, A Characterization for the Length of Cycles of the N-Number Ducci Game. Fibonacci Quarterly, volume 43, no1, 53-59, (2005).
[5] J. Creely, The Length of a Three-Number Game. Fibonacci Quarterly, volume 26, no2, 141-143, (1988).
[6] A. Ehrlich, Periods in Ducci’s n-Number Game of Differences. Fibonacci Quarterly, volume 28, no4, 302-305, (1990)
[7] A. Ludington-Young, Ducci-Processes of 5-Tuples. Fibonacci Quarterly, volume 36, no5, 419-434, (May 1998)
[8] A. Ludington-Young, Length of the 7-Number Game. Fibonacci Quarterly, volume 26, no3,195-204, (1998).
[9] A. Ludington-Young, Length of the n-Number Game. Fibonacci Quarterly, volume 28, no3, 259-265, (1990).
[10] W. Webb, The Length of the Four-Number Game. Fibonacci Quarterly, volume 20, no1, 33-35, (1982).
[11] F.B. Wong, Ducci Processes. Fibonacci Quarterly, volume 20, no2, 97-105, (1982).
[12] 蔡秀芬, Diffy Box (狄菲方塊). National Chengchi University, (2008)
描述 碩士
國立政治大學
應用數學系數學教學碩士在職專班
99972015
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099972015
資料類型 thesis
dc.contributor.advisor 李陽明zh_TW
dc.contributor.author (Authors) 黃信弼zh_TW
dc.creator (作者) 黃信弼zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 1-Nov-2012 13:58:08 (UTC+8)-
dc.date.available 1-Nov-2012 13:58:08 (UTC+8)-
dc.date.issued (上傳時間) 1-Nov-2012 13:58:08 (UTC+8)-
dc.identifier (Other Identifiers) G0099972015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/55132-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系數學教學碩士在職專班zh_TW
dc.description (描述) 99972015zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 在迪菲方塊中，我們將正方形的四個頂點皆填入數值，再利用相鄰兩頂點相減，再取絕對值的方式觀察其數列行為，發現四個頂點的數字最後皆會收斂至0。在本文中，我們將之推廣至五邊形，我們稱它為迪菲五邊形。我們套用同樣的運算模式後，發現亦有特殊的收斂行為。zh_TW
dc.description.abstract (摘要) In Diffy box, we write down numbers on the four vertices of square, and then on the midpoint of each side write the difference between the two numbers at its endpoints. It is known that the numbers on the four vertices of a square will converge to zero finally. In this article, we use the same operations as Diffy box to discuss pentagons which we call" Diffy pentagon ". We find it will converge, too.en_US
dc.description.tableofcontents Abstract ----------------------------------------------------------------- i

中文摘要 ----------------------------------------------------------------------- ii

Chapter 1 Introduction ---------------------------------------------- 1

Chapter 2 The Description of the Convergence Properties -------- 2

2.1 Definitions and Theorems ----------------------------- 2

2.2 Description of Feature ----------------------------------- 8

Chapter 3 Pentagon with Cycle Convergence ------------------------- 11

3.1 Introduction ----------------------------------------------- 11

3.2 The Proof with Strong Induction ------------------------ 11

Chapter 4 Conclusion and Promotion ---------------------------------- 23

Appendix -------------------------------------------------------------------- 24

References ------------------------------------------------------------------- 26		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099972015en_US
dc.subject (關鍵詞) 迪菲五邊形zh_TW
dc.subject (關鍵詞) 強勢數學歸納法zh_TW
dc.subject (關鍵詞) Diffy pentagonen_US
dc.subject (關鍵詞) Strong inductionen_US
dc.title (題名) 迪菲方塊zh_TW
dc.title (題名) Diffy Pentagonen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] A. Behn, C. Kribs-Zaleta, and V. Ponomarenko, The Convergence of Difference Boxes. American Math. Monthly, volume 112, 426-438, (1995)
[2] F. Breuer, Ducci Sequences in Higher Dimensions. Electronic Journal of Combinatorial
Number Theory 7, #A24, (2007)
[3] R. Brown and J. Merzel, The Length of Ducci’s Four-Number Game. Rocky Mountain
Journal of Mathematics, volume37, 45-65, (2007)
[4] N. Calkin, J. Stevens, and D. Thomas, A Characterization for the Length of Cycles of the N-Number Ducci Game. Fibonacci Quarterly, volume 43, no1, 53-59, (2005).
[5] J. Creely, The Length of a Three-Number Game. Fibonacci Quarterly, volume 26, no2, 141-143, (1988).
[6] A. Ehrlich, Periods in Ducci’s n-Number Game of Differences. Fibonacci Quarterly, volume 28, no4, 302-305, (1990)
[7] A. Ludington-Young, Ducci-Processes of 5-Tuples. Fibonacci Quarterly, volume 36, no5, 419-434, (May 1998)
[8] A. Ludington-Young, Length of the 7-Number Game. Fibonacci Quarterly, volume 26, no3,195-204, (1998).
[9] A. Ludington-Young, Length of the n-Number Game. Fibonacci Quarterly, volume 28, no3, 259-265, (1990).
[10] W. Webb, The Length of the Four-Number Game. Fibonacci Quarterly, volume 20, no1, 33-35, (1982).
[11] F.B. Wong, Ducci Processes. Fibonacci Quarterly, volume 20, no2, 97-105, (1982).
[12] 蔡秀芬, Diffy Box (狄菲方塊). National Chengchi University, (2008)		zh_TW