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https://ah.lib.nccu.edu.tw/handle/140.119/55132| 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 | 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)\n[2] F. Breuer, Ducci Sequences in Higher Dimensions. Electronic Journal of Combinatorial \nNumber Theory 7, #A24, (2007)\n[3] R. Brown and J. Merzel, The Length of Ducci’s Four-Number Game. Rocky Mountain \nJournal of Mathematics, volume37, 45-65, (2007) \n[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). \n[5] J. Creely, The Length of a Three-Number Game. Fibonacci Quarterly, volume 26, no2, 141-143, (1988).\n[6] A. Ehrlich, Periods in Ducci’s n-Number Game of Differences. Fibonacci Quarterly, volume 28, no4, 302-305, (1990)\n[7] A. Ludington-Young, Ducci-Processes of 5-Tuples. Fibonacci Quarterly, volume 36, no5, 419-434, (May 1998)\n[8] A. Ludington-Young, Length of the 7-Number Game. Fibonacci Quarterly, volume 26, no3,195-204, (1998).\n[9] A. Ludington-Young, Length of the n-Number Game. Fibonacci Quarterly, volume 28, no3, 259-265, (1990).\n[10] W. Webb, The Length of the Four-Number Game. Fibonacci Quarterly, volume 20, no1, 33-35, (1982). \n[11] F.B. Wong, Ducci Processes. Fibonacci Quarterly, volume 20, no2, 97-105, (1982).\n[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 |
| Appears in Collections: | 學位論文 |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| 201501.pdf | 842.85 kB | Adobe PDF2 | View/Open |
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