卡塔蘭多面體的動態幾何作圖法; Construction of Catalan Solids

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/48294

Title:	卡塔蘭多面體的動態幾何作圖法;Construction of Catalan Solids
Authors:	阮賢彧;Hsien-Yu Juan
Contributors:	數學研究所
Keywords:	動態幾何;卡塔蘭;作圖法;Catalan;cabri
Date:	2011-07-20
Issue Date:	2012-01-05 14:44:22 (UTC+8)
Abstract:	此論文主要為藉由Cabri3D來簡便製作卡塔蘭多面體，並一起做出跟其對偶的阿基米德多面體；以觀看二者的圖形關係。其次，以作圖過程來觀察其對稱性，以及一致性。卡塔蘭多面體共有13種，但其中的五角化二十四面體與五角化六十面體由於無法只由尺規製作呈現，故將此兩種剃除；其餘共剩下11種。雖是先由阿基米德多面體再依對偶才衍生出卡塔蘭多面體，但本作圖法是先直接做出卡塔蘭多面體；再依對偶定義作出阿基米德多面體，爾後憑藉Cabri3D來確認其真為卡塔蘭多面體。本篇第一章節先說明11種阿基米德多面體資訊，及各形成的原因。第二章節說明卡塔蘭多面體的資訊與對偶的定義。第三章第一節便開始進入卡塔蘭作圖法；及第二節的依對偶定義所作出的阿基米德多面體。第四章便將在作圖過程中發現的某些卡塔蘭多面體的關係一致性作說明。 This paper aims at the construction of Catalan solids by Cabri3D, and the construction of Archimedean solids altogether; and then to observe the graphic relationship between Catalan solids and Archimedean solids. Second, to observe the symmetry, and unity by the processes. There are total 13 Catalan solids, but there is no method about constructions of pentagonal icositetrahedron and pentagonal hexecontahedron by ruler gauge,so the remainder are 11 Catalan solids. Archimedean solids product Catalan solids by dual definition, but I draw Catalan solids first; Archimedean solids second by dual definition, and confirm Catalan solids by Cabri3D. Chapter 1 is informations of Archimedean solids, and their reason of construction. Chapter 2 is informations of Catalan solids, and the dual definition. Chapter 3 is constructions of Catalan solids by Cabri3D. Chapter 4 is unities of some Catalan solids.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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