非自相交的龙曲线

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series Pub Date : 2025-03-24 DOI:10.1016/j.indag.2025.03.006

Shigeki Akiyama , Yuichi Kamiya , Fan Wen

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引用次数: 0

摘要

让我们将一张纸沿同一方向折叠多次，然后将其展开，在所有折痕处形成一个固定的角度θ。得到的形状称为展开角为θ的龙曲线。当0≤θ<；90°时，对应的龙曲线有自交。当θ=180°时，对应的龙曲线为直线，没有自交。在本文中，我们将证明任何展开角大于99.3438°且小于180°的Dragon曲线都不存在自交。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Non-self-intersective Dragon curves

Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle

θ

at all creases. The resulting shape is called the Dragon curve with the unfolding angle

θ

. When

0 \leq θ < 90 °

, the corresponding Dragon curve has a self-intersection. When

θ = 180 °

, the corresponding Dragon curve is a straight line, which has no self-intersection. In this paper, we will show that any Dragon curve whose unfolding angle is greater than

99.3438 °

and less than

180 °

has no self-intersection.

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来源期刊

Indagationes Mathematicae-New Series 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

79 days

期刊介绍： Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.