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一、前言在折纸数理学中,芳贺第一定理是指将一张正方形纸的右下顶点C翻折至上边AB中点C’时,底边CD的翻折线C’D’与AD的交点G是AD的三等分点(如图1);芳贺第二定理是指将一张正方形纸的右上顶点B以右下顶点C与上边AB中点E的连线段为折痕翻折至B’时,EB’的延长线与AD的交点H是AD的三等分点(如图2).文[1]对芳贺第一定理进行了三个方面的一般化,笔者受其启发,对第二个方面的一般化(正方形→长方形)进行更深入地探究,并将探究扩展到芳贺第二定理上,期
I. INTRODUCTION In origami mathematics, the first theorem of Nakagawa means folding the lower right vertex C of a square paper to the midpoint C’ of the upper side AB, and the folding line C’D’ of the bottom edge CD and AD. The intersection point G is the three-divisional point of AD (Fig. 1); the second-principle of Fangza is the crease of the top-right vertex B of a square paper with the connecting line segment of the lower-right vertex C and the middle point AB of the upper edge AB. When turning over to B’, the intersection point between the extension line of EB’ and AD is the third division point of AD (see Fig. 2). [1] generalized the first theorem of Fang He in three aspects. The author was inspired by this and conducted a deeper exploration of the generalization of the second aspect (square→rectangle), and extended the exploration to the second theorem of Nakagawa.