Non-self-intersective dragon curves
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866910888956526592 |
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| author | Akiyama, Shigeki Kamiya, Yuichi Wen, Fan |
| author_facet | Akiyama, Shigeki Kamiya, Yuichi Wen, Fan |
| contents | 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 $0\leθ<90^{\circ}$, the corresponding Dragon curve has a self-intersection. When $θ=180^{\circ}$, 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 $99.3438^{\circ}$ and less than $180^{\circ}$ has no self-intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-self-intersective dragon curves Akiyama, Shigeki Kamiya, Yuichi Wen, Fan Metric Geometry 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 $0\leθ<90^{\circ}$, the corresponding Dragon curve has a self-intersection. When $θ=180^{\circ}$, 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 $99.3438^{\circ}$ and less than $180^{\circ}$ has no self-intersection. |
| title | Non-self-intersective dragon curves |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2401.07002 |