Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/61519


Title: 一個點線面的切割問題
A Partition Problem with Points,Lines and Planes
Authors: 李昱欣
Li, Yu Shin
Contributors: 李陽明
李昱欣
Li, Yu Shin
Keywords: 切割問題
點線面
Partition Problem
Points,Lines,and Planes
Date: 2013
Issue Date: 2013-11-01 11:49:23 (UTC+8)
Abstract: 在這篇論文中,我們希望用不同角度來重新探討一個古典的數學問題;點、線、面切割最多區域問題,雖然這個問題已經經由許多方法得到公式,例如:遞迴關係、差分方程式、歐拉公式、標準n維空間切割系統等等,並延伸出其他方面的問題,可以運用在很多地方,所以我們希望可以再找到更簡單易懂的論證方式,可以讓國中學生也能理解。
思考學生現有的數學觀念,我們發現利用不等式的數學觀念,藉由定義出一套有規則的系統以及數學歸納法,可以以更直接,簡單的理論驗證出此數學公式,最後我們更希望能將這理論推廣至n維度空間。
In this research, we will discuss a classical mathematical question from different aspects. The question of maximizing the number of regions made up by points, lines and planes has been proved and developed many formulas, using Recurrence Relations, Difference Equations, and Euler's Formula etc., which can extend to other questions and apply to many areas. Therefore, we hope to find an easier way to prove it which may help middle school students to understand better.
We find that we can use the concept of inequality from what the students learn so far. By defining a logical system and using Induction, we can prove this mathematical formula in an easier and more direct way. Finally we hope it can be generalized to n-dimensional space.
Reference: [1]Stephen H. Friedberg, Arnold J. Insel, and Lawerence E. Spence, Linear Algebra, 3rd ed.,Prentice-Hall,1997,47-48.
[2]Alan Tucker (2007,5th edition). Applied Combinatorics. John Wiley & Sons Inc.
[3] Grimaldi, R. P., Recurrence relations. In Handbook of Discrete and Combinatorial
Mathematics by Rosen, K. H. (Editor). Boca Raton, Florida: CRC, 1999.
[4]王佑欣,民國91年(2002),Combinatorial Argument of Partition with Point ,Line and Space,政大應數所碩士論文。
[5]何景國,差分法及其在組合學上的應用,數學傳播第10卷第一期,頁49-51。
[6]宋秉信,從尤拉公式到空間的平面分割,數學傳播,第22卷第三期,頁54-60。
[7]游森棚,披薩與西瓜,科學月刊第477期,頁60-62。
[8]游森棚,談談九十五學年度高中數學新課程大綱的“遞迴”。2008 February 25。Available from:
http://umath.nuk.edu.tw/_senpengeu/HighSchool/recurr.pdf
Description: 碩士
國立政治大學
應用數學系數學教學碩士在職專班
100972007
102
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0100972007
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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