How many ways can a convex polygon of n（≥3） sides be triangulated by diagonals that do not intersect？ The problem was first proposed by Leonard Euler. Instead of setting up a recurrence relation and using the method of generating function to solve it, we shall set up a one-to-one correspondence between the convex-polygon triangulations we are trying to count the rooted binary trees that have already been counted. Let bn denote the number of rooted ordered binary trees with n vertices and let tn denote the number of triangulations of convex polygon with n sides. We conclude that tn＝bn＝1/(n-1) ((2n-4)¦(n-2)).

本研究旨在探討不同年齡層的幼兒在基本幾何圖形的辨識情況，並分析幼兒辨識三角形及圓形的影響向度。 研究工具參考自「吳氏視覺的幾何思考層次測驗」，研究對象採便利取樣，選取幼稚園小、中、大班的幼兒(大班359位，中班290位，小班121位。共770位)。進行三角形和圓形的辨識，本研究將會影響幼兒辨識三角形和圓形的向度分為六大類：直線或曲線、開放或封閉、不同大小、不同方位、角度、凹凸。研究結果顯示： (1)不同大小、不同方位、角度這三種向度對幼兒而言的辨識度是較低的。 (2)直線或曲線、開放或封閉、凹凸這三種向度對幼兒而言的辨識度是較高的。(3)最影響幼兒辨識圖形的向度為凹凸的圖形。 (4)圖形越大，幼兒的辨識度就越高，圖形越小，幼兒的辨識度就越低。 (5)邊長比例越懸殊的三角形，幼兒就越不容易辨識出來。 (6)年齡層越高的幼兒，對於圖形的辨識率就越高。 / The purpose of the research is to analyze the ability of how young children at different ages recognize basic geometric figures, and to find out the factors which influence their recognition of triangles and circles. “Wu's Test of Geometric Thinking of Visual Level” was adopted here as the main research tool. 770 subjects were chosen by convenience sampling, including 359 from top classes, 290 from middle classes, and 121 from the bottom classes in kindergartens. To study how young children recognize triangles and circles, the factors were divided into six dimensions: (1) straight line or curve line; (2) open or close figure; (3) figures of different sizes; (4) figures of different positions; (5) figures of different angles; and (6) convex or concave figures. Here are the research findings: (1) Among six dimensions, it is more difficult for children to recognize figures of different sizes, positions and angles. (2) While the other three dimensions including “straight line or curve line”, “open or close figure”, and “convex or concave figures” are more easily to be recognized by children. (3) It is most difficult for children to recognize convex or concave figures. (4) Bigger figures are more easily and accurately recognized by children then smaller ones. (5) With higher side ratio of triangles, it’s more difficult for children to recognize them. (6) Elder children can recognize figures more easily and successfully than younger children.

本論文採取歷史文獻分析與理解社會學(verstehende Soziologie)的研究途徑，從「以中國說中國」的方法入手，重視歷史事實作為論證基礎的功能與意義。 對中共「民主集中制」的研究在廣度與深度上都超乎中國大陸內部與外部學者在這方面的論述，系統化地借助中共黨史反映了民主集中制一般不為人所注意的關鍵面向。對民主集中制之作用的分析引導筆者發現，中國大陸總體面出現一個「黨、國家、社會」的三角形，這是在現階段與可預見之未來的人類文明中一個非常態的國家總體結構。筆者進而對照西方權力制衡的理論，反映出在民主集中制下是不可能發展出真正的權力制約與監督的機制的，民主集中制的內涵處處體現「一元化整體性控制意識」，民主與民主集中制之間無論就理論或現實運作都存在不可調和的矛盾。 改革開放以來的中共文化戰略奠基者為鄧小平，他的基本方法是將重心放在寄望以經濟建設的成果支持行為層面的紀律，進而鞏固精神思想層面的意識形態。順此，他主張「不搞爭論」與「堅持四項基本原則」，希望大力發展生產力，強調的是「工具理性」。這些其實都是受民主集中制之「一元化整體性控制意識」的影響。 筆者採用各種型態的資料與具體數據說明「『民主集中制』對文化戰略的影響」與「『民主集中制』對改革開放以來文化戰略與戰略造成的困難與挑戰」，呈現出中共文化戰略的不合理與不合時的性質。從文化戰略的視角可以看到許多中國大陸現今不易從單純的政治、經濟、社會的角度所能觀察到的問題。本論文針對此方面的解決方案與方向提出了一些線索與頭緒。 最後，解釋在第一章提出之胡錦濤表現的反差現象。其次，論證中國大陸的政治體制改革應為不可迴避的必要之務，民主改革未必對中共不利，可能更有利。同時回答第一章中共如何統治的問題。 / Adopting the approaches of historical document analyses and understanding sociology, this dissertation brings the method of explaining China in terms of China into bear and places importance on the function and meaning of historical facts as the departing basis of its discussions. Based on the Chinese Communist Party’s (the CCP hereafter) history, the dissertation systematically presents some key points of the CCP’s democratic centralism, to which attention was not paid. It shows wider and deeper understanding of the CCP’s democratic centralism. The understanding leads the author to notice the “party, state and society” triangle, which reflects the uniqueness of the structure of China as a country in the contemporary world. The CCP’s democratic centralism reflects “consciousness of unitary holistic control” and is in fact incompatible with democracy by its normal definition in respect of theory and practice. The foundation of the CCP’s cultural development since the reform and opening was laid by Deng Xiaoping, whose methodology laid stress on economic development. Deng hoped to accomplish some economic achievements to secure behavioral discipline among people and finally consolidate the party’s ideologies and theories. He therefore advocated “no disputes” and “insistence on four fundamental principles” and did his best to promote development of productivity, namely instrumental rationality. All he did embodied “consciousness of unitary holistic control,” so has the CCP’s cultural strategies done the same. Basing on different types of materials and data, the author analyzed the influences of the CCP’s democratic centralism on its cultural strategies and presented the difficulties and challenges to the strategies caused by the democratic centralism since the reform and opening. In the final chapter, the author explained Hu Jintao’s surprising reaction and answered the question how the CCP has been ruling the country. Both were mentioned in Chapter one.