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| 研究生： |
黃信弼 |
|---|---|
| 論文名稱： |
迪菲五邊形 Diffy Pentagon |
| 指導教授： | 李陽明 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系數學教學碩士在職專班 |
| 論文出版年： | 2012 |
| 畢業學年度： | 101 |
| 語文別： | 英文 |
| 論文頁數： | 26 |
| 中文關鍵詞： | 迪菲五邊形 、強勢數學歸納法 |
| 外文關鍵詞： | Diffy pentagon, Strong induction |
| 相關次數： | 點閱：152 下載：34 |
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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.
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
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