DIFFY HEPTAGON

• Main Author: 林亨峰
• Other Authors: 李陽明
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/03900824493587254133

碩士 === 國立政治大學 === 應用數學系數學教學碩士在職專班 === 102 === In a Diffy Box, after limited steps of calculations, the result converges to all zeros. This essay is commissioned to expand Diffy Box’s square to heptagon, which we call “Diffy Heptagon”. We will discuss if Diffy Heptagon shows the same convergence, or the existence of other result? This article is proved with Strong Induction. The result shows that a Diffy Heptagon will present three types of convergence after limited operations. Moreover, we extend the nonnegative integers to integers and rational numbers. The conclusion is, regardless of the numbers, what we obtain is isomorphic or similar convergence. Finally, we propose some issues and suggestions. For examples, what type of numbers we label individually will cause class I, class II or class III convergence? In addition to the zero convergence, what is the connection between the labeled numbers and other convergence types? All those questions are worth studying Diffy Heptagon even further.