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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05583 |
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| _version_ | 1866917688713936896 |
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| author | Ozkaraca, Mustafa Ismail |
| author_facet | Ozkaraca, Mustafa Ismail |
| contents | Can you stretch and reform a curve such that it fills a square completely? This question dates back to 18th century, the origin of space-filling curves. It was proved affirmatively by many great mathematicians. In this document, we reconsider the problem and present a different proof using Cartesian product of Fibonacci substitution with itself. Our construction differs from other curves by design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Fibonacci Space-Filling Curve Ozkaraca, Mustafa Ismail Geometric Topology Can you stretch and reform a curve such that it fills a square completely? This question dates back to 18th century, the origin of space-filling curves. It was proved affirmatively by many great mathematicians. In this document, we reconsider the problem and present a different proof using Cartesian product of Fibonacci substitution with itself. Our construction differs from other curves by design. |
| title | The Fibonacci Space-Filling Curve |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2406.05583 |